Power allocation in a wireless communication system

ABSTRACT

Systems and methodologies are described that facilitate allocating power levels in a wireless communication network. A metric based upon spectral efficiency can be employed in connection with optimizing power allocation. Further, power for transmitters to utilize can be assigned as a function of time. Moreover, a single sub-carrier network and/or a multiple sub-carrier networks can leverage one or more power allocation schemes.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Patentapplication Ser. No. 60/844,817 entitled “POWER ALLOCATION IN A WIRELESSCOMMUNICATION SYSTEM” which was filed Sep. 14, 2006 and U.S. ProvisionalPatent application Ser. No. 60/848,041 entitled “FRACTIONAL POWER REUSEIN A MULTICARRIER DOWNLINK” which was filed Sep. 26, 2006. Theentireties of the aforementioned applications are herein incorporated byreference.

BACKGROUND

I. Field

The following description relates generally to wireless communications,and more particularly to allocating power for transmitters insingle-carrier or multi-carrier wireless communication systems.

II. Background

Wireless communication systems are widely deployed to provide varioustypes of communication; for instance, voice and/or data can be providedvia such wireless communication systems. A typical wirelesscommunication system, or network, can provide multiple users access toone or more shared resources. For instance, a system can use a varietyof multiple access techniques such as Frequency Division Multiplexing(FDM), Time Division Multiplexing (TDM), Code Division Multiplexing(CDM), Orthogonal Frequency Division Multiplexing (OFDM), and others.

Common wireless communication systems employ one or more base stationsthat provide a coverage area. A typical base station can transmitmultiple data streams for broadcast, multicast and/or unicast services,wherein a data stream can be a stream of data that can be of independentreception interest to a wireless terminal. A wireless terminal withinthe coverage area of such base station can be employed to receive one,more than one, or all the data streams carried by the composite stream.Likewise, a wireless terminal can transmit data to the base station oranother wireless terminal.

According to an example, a transmitter in a wireless communicationsystem can utilize one or multiple sub-carriers for transmission. For asingle transmitter with multiple sub-carriers, for instance, power canbe efficiently allocated by evenly spreading power across thesub-carriers assuming that the channel is stationary (e.g., due toconcavity of the Shannon capacity). However, when a second transmitteris introduced that transmits simultaneously as the first transmitter andtherefore causes the transmitters to interfere with one another, theforegoing no longer holds true. For instance, when mobile devices aresituated at the boundary of two cells, such devices can operate below 0dB and thus experience significant diminution in quality of service.Moreover, when a single sub-carrier is employed by multiple interferingtransmitters, similar inefficiencies and/or degraded service due tointerference can commonly be experienced in connection with conventionalpower allocation techniques.

SUMMARY

The following presents a simplified summary of one or more embodimentsin order to provide a basic understanding of such embodiments. Thissummary is not an extensive overview of all contemplated embodiments,and is intended to neither identify key or critical elements of allembodiments nor delineate the scope of any or all embodiments. Its solepurpose is to present some concepts of one or more embodiments in asimplified form as a prelude to the more detailed description that ispresented later.

In accordance with one or more embodiments and corresponding disclosurethereof, various aspects are described in connection with facilitatingallocation of power levels in a wireless communication network. A metricbased upon spectral efficiency can be employed in connection withoptimizing power allocation. Further, power for transmitters to utilizecan be assigned as a function of time. Moreover, a single sub-carriernetwork and/or a multiple sub-carrier networks can leverage one or morepower allocation schemes.

According to related aspects, a method that facilitates operating acommunication network including a first wireless communication basestation that includes a first sector is described herein. The method caninclude transmitting on a first channel at a first power level from thefirst sector during a first time period based on a first predeterminedpattern, the first channel including a first frequency bandwidth.Further, the method can comprise transmitting on the first channel at asecond power level from the first sector during a second time periodbased on the first predetermined pattern, the second power level is atleast 0.5 dB different from the first power level.

Another aspect relates to a wireless communications apparatus. Thewireless communications apparatus can include a memory that retainsinstructions related to transmitting on a first channel at a first powerlevel from a first sector during a first time period based on a firstpredetermined pattern and transmitting on the first channel at a secondpower level from the first sector during a second time period based onthe first predetermined pattern, the second power level is at least 0.5dB different from the first power level. Moreover, the wirelesscommunications apparatus can include a processor, coupled to the memory,configured to execute the instructions retained in the memory.

Yet another aspect relates to a wireless communications apparatus thatenables communicating with allocated power levels. The wirelesscommunications apparatus can include means for transmitting on a firstchannel at a first power level from a first sector during a first timeperiod based on a first predetermined pattern, the first channelincluding a first frequency bandwidth. Moreover, the wirelesscommunications apparatus can comprise means for transmitting on thefirst channel at a second power level from the first sector during asecond time period based on the first predetermined pattern, the secondpower level is at least 0.5 dB different from the first power level.

Still another aspect relates to a machine-readable medium having storedthereon machine-executable instructions for transmitting on a firstchannel at a first power level from a first sector during a first timeperiod based on a first predetermined pattern, the first channelincluding a first frequency bandwidth; and transmitting on the firstchannel at a second power level from the first sector during a secondtime period based on the first predetermined pattern, the second powerlevel is at least 0.5 dB different from the first power level.

In accordance with another aspect, an apparatus in a wirelesscommunication system can include a processor, wherein the processor canbe configured to transmit on a first channel at a first power levelduring a first time period based on a first predetermined pattern, thefirst channel including a first frequency bandwidth. Further, theprocessor can be configured to transmit on the first channel at a secondpower level during a second time period based on the first predeterminedpattern, the second power level is at least 0.5 dB different from thefirst power level.

To the accomplishment of the foregoing and related ends, the one or moreembodiments comprise the features hereinafter fully described andparticularly pointed out in the claims. The following description andthe annexed drawings set forth in detail certain illustrative aspects ofthe one or more embodiments. These aspects are indicative, however, ofbut a few of the various ways in which the principles of variousembodiments may be employed and the described embodiments are intendedto include all such aspects and their equivalents.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an illustration of a wireless communication system inaccordance with various aspects set forth herein.

FIG. 2 is an illustration of an example system that enables controllingpower allocation for transmission within a cell or sector.

FIG. 3 is an illustration of an example system that allocates powerlevels in a multiple sub-carrier network.

FIG. 4 is an illustration of example even power level allocation schemefor a multiple sub-carrier system.

FIG. 5 is an illustration of an example time varying power allocationscheme for a multiple sub-carrier system.

FIG. 6 is an illustration of an example time varying power allocationscheme for a multiple sub-carrier environment.

FIG. 7 is an illustration of an example time varying power allocationscheme for a single carrier system.

FIG. 8 is an illustration of an example time varying power allocationscheme for a single carrier cellular data network.

FIG. 9 is an illustration of an example sector-wise reuse multi-celldeployment in accordance with various aspects of the claimed subjectmatter.

FIG. 10 is an illustration of an example cell-wise reuse deployment ofmultiple cells for a power allocation reuse scheme.

FIG. 11 is an illustration of an example power allocation scheme for usewith differing sectors according to various aspects of the claimedsubject matter.

FIG. 12 is an illustration of an example scheme that includes smoothpower variation curves (e.g., power allocation curves, smooth powerallocation pattern curves, . . . ) for disparate sectors (and/or cells).

FIG. 13 is an illustration of another example power allocation scheme inaccordance with various aspects of the claimed subject matter.

FIG. 14 is an illustration of an example diagram of a capacity regionfor a two-user two-carrier single-cell system under a fixed powerallocation.

FIG. 15 is an illustration of an example graphical depiction of a proofin accordance with various aspects of the claimed subject matter.

FIG. 16 is an illustration of an example diagram of a capacity region of(P₁, P₂) as compared to reuse-1.

FIG. 17 is an illustration of an example diagram of capacity regionsunder reuse-1, general time/power sharing and superposition.

FIG. 18 is an illustration of an example diagram of capacity regions fora two-user two-carrier two-cell system under reuse-1, reuse-2 and a (P₁,P₂) allocation.

FIG. 19 is an illustration of an example diagram of various capacityregions.

FIG. 20 is an illustration of an example diagram representing anachievable rate region under opportunistic power allocation.

FIG. 21 is an illustration of an example diagram depicting channelconditions for two users within a cell under breathing cells where bothchannel gains can be normalized by the average channel gain of the gooduser.

FIG. 22 is an illustration of an example diagram depicting a channelcondition and normalized schedulable rate for different users in abreathing-cell scheme.

FIG. 23 is an illustration of an example methodology that facilitatesoperating a communication network including a wireless communicationbase station that includes a first sector.

FIG. 24 is an illustration of an example methodology that facilitatesadaptively assigning power allocation patterns for allocating powerlevels.

FIG. 25 is an illustration of an example methodology that facilitatesoperating a multiple carrier communication network including a firstwireless communication base station that includes a first sector.

FIG. 26 is an illustration of an example communication systemimplemented in accordance with various aspects including multiple cells.

FIG. 27 is an illustration of an example base station in accordance withvarious aspects.

FIG. 28 is an illustration of an example wireless terminal (e.g., mobiledevice, end node, . . . ) implemented in accordance with various aspectsdescribed herein.

FIG. 29 is an illustration of an example system that enablescommunicating with allocated power levels.

FIG. 30 is an illustration of an example system that enablescommunicating with allocated power levels in a multiple carrier wirelesscommunication network.

DETAILED DESCRIPTION

Various embodiments are now described with reference to the drawings,wherein like reference numerals are used to refer to like elementsthroughout. In the following description, for purposes of explanation,numerous specific details are set forth in order to provide a thoroughunderstanding of one or more embodiments. It may be evident, however,that such embodiment(s) may be practiced without these specific details.In other instances, well-known structures and devices are shown in blockdiagram form in order to facilitate describing one or more embodiments.

As used in this application, the terms “component,” “module,” “system,”and the like are intended to refer to a computer-related entity, eitherhardware, firmware, a combination of hardware and software, software, orsoftware in execution. For example, a component may be, but is notlimited to being, a process running on a processor, a processor, anobject, an executable, a thread of execution, a program, and/or acomputer. By way of illustration, both an application running on acomputing device and the computing device can be a component. One ormore components can reside within a process and/or thread of executionand a component may be localized on one computer and/or distributedbetween two or more computers. In addition, these components can executefrom various computer readable media having various data structuresstored thereon. The components may communicate by way of local and/orremote processes such as in accordance with a signal having one or moredata packets (e.g., data from one component interacting with anothercomponent in a local system, distributed system, and/or across a networksuch as the Internet with other systems by way of the signal).

Furthermore, various embodiments are described herein in connection witha wireless terminal. A wireless terminal can also be called a system,subscriber unit, subscriber station, mobile station, mobile, mobiledevice, remote station, remote terminal, access terminal, user terminal,terminal, wireless communication device, user agent, user device, oruser equipment (UE). A wireless terminal may be a cellular telephone, acordless telephone, a Session Initiation Protocol (SIP) phone, awireless local loop (WLL) station, a personal digital assistant (PDA), ahandheld device having wireless connection capability, computing device,or other processing device connected to a wireless modem. Moreover,various embodiments are described herein in connection with a basestation. A base station may be utilized for communicating with wirelessterminal(s) and may also be referred to as an access point, Node B, orsome other terminology.

Moreover, various aspects or features described herein may beimplemented as a method, apparatus, or article of manufacture usingstandard programming and/or engineering techniques. The term “article ofmanufacture” as used herein is intended to encompass a computer programaccessible from any computer-readable device, carrier, or media. Forexample, computer-readable media can include but are not limited tomagnetic storage devices (e.g., hard disk, floppy disk, magnetic strips,etc.), optical disks (e.g., compact disk (CD), digital versatile disk(DVD), etc.), smart cards, and flash memory devices (e.g., EPROM, card,stick, key drive, etc.). Additionally, various storage media describedherein can represent one or more devices and/or other machine-readablemedia for storing information. The term “machine-readable medium” caninclude, without being limited to, wireless channels and various othermedia capable of storing, containing, and/or carrying instruction(s)and/or data.

Referring now to FIG. 1, a wireless communication system 100 isillustrated in accordance with various embodiments presented herein.System 100 can comprise one or more base stations 102 (e.g., accesspoints) in one or more sectors that receive, transmit, repeat, etc.,wireless communication signals to each other and/or to one or moremobile devices 104. Each base station 102 can comprise a transmitterchain and a receiver chain, each of which can in turn comprise aplurality of components associated with signal transmission andreception (e.g., processors, modulators, multiplexers, demodulators,demultiplexers, antennas, . . . ) as will be appreciated by one skilledin the art. Mobile devices 104 can be, for example, cellular phones,smart phones, laptops, handheld communication devices, handheldcomputing devices, satellite radios, global positioning systems, PDAs,and/or any other suitable device for communicating over wirelesscommunication system 100. Base stations 102 can each communicate withone or more mobile devices 104. Base stations 102 can transmitinformation to mobile devices 104 over a forward link (downlink) andreceive information from mobile devices 104 over a reverse link(uplink).

Base stations 102 and mobile devices 104 can utilize one or multiplesub-carriers for communication there between. By way of illustration, aplurality of base stations 102 can each utilize a common sub-carrier ora common set of sub-carriers for downlink transmission. Additionally oralternatively, a common sub-carrier or set of sub-carriers can beutilized for uplink transmission (e.g., in one or multiple cells orsectors) by mobile devices 104 that can interfere with one another.

System 100 can support differing types of users such as close-to-basestation users and cell-boundary users. For close-to-base station userswho may not be affected by inter-cell interference, even transmit powerallocation across different carriers or frequency subbands can be morefavorable since it offers more segments (or degrees of freedom).Meanwhile, cell-boundary users can benefit from schemes like simplefrequency-reuse whereby some sub-carriers in each sector can be shut offsince such a scheme can offer signal-to-noise (SNR) improvement that cancompensate for the segment loss. When a mixture of users exists, theoverall system throughput can be optimized (e.g., maximized) byassigning different powers to different carriers or frequency subbands.

More particularly, system 100 can employ a time-varying power allocationscheme to leverage time flexibility to improve spectral efficiency,where the power allocation changes over time according to apre-determined pattern. Various example power allocation schemes areprovided below in accordance with various aspects of the claimed subjectmatter. Moreover, examples described herein relate to OFDM systems;however, it is to be appreciated that concepts provided herein can beapplied to systems that leverage differing types of technologies (e.g.,CMDA systems, GSM system, . . . ).

With reference to FIG. 2, illustrated is an example system 200 thatenables controlling power allocation for transmission within a cell orsector. System 200 includes a base station 202 that can communicate withone or more mobile devices 204-206 (e.g., mobile device 1 204, . . . ,mobile device N 206, where N can be substantially any integer). Basestation 202 can further include a power allocator 208 and a clock 210.Power allocator 208 can employ one or more of the example powerallocation schemes described herein. Such schemes can enable optimizingperformance (e.g., spectral efficiency) associated with a network.Moreover, power allocator 208 can utilize timing information obtained byclock 210 to schedule transmission (e.g., downlink transmission frombase station 202 to one or more mobile devices 204-206, uplinktransmission from mobile device 204-206 to base station 202, . . . ).For instance, timing information can be leveraged along with the powerallocation scheme to select an identity of a transmitter and/or receiveras well as a power level to be utilized for transmission during aparticular time slot.

According to an example, system 200 can be a single carrier system;thus, a common carrier can be employed for communicating between basestation 202 and mobile device(s) 204-206 (as well as for similarcommunication in disparate sector(s) and/or cell(s)). Base station 202can be coordinated with disparate base stations (not shown) to implementa particular power allocation scheme; hence, power levels fortransmission over the common carrier can be assigned by power allocator208 as a function of time determined by clock 210.

By way of illustration, power allocator 208 can assign a particularpower level from a set of M discrete power levels, where M can besubstantially any integer (e.g., employing the example schemes in FIGS.7-8, 11). Base station 202 can utilize a set of discrete power levelsthat can be substantially similar to set(s) employed by disparate basestations in the network and/or the sets of discrete power levels candiffer between base stations. According to an example, base station 202can employ a set of discrete power levels that includes P₁ and P₂, whilea neighboring base station (not shown) can utilize a set of discretepower levels that includes P₃ and P₄. For instance, P₁ can be equal toP₄ and P₂ can be equal to P₃; yet, it is contemplated that such powerlevels can differ from one another. Additionally or alternatively, P₁can be larger than P₂ and P₄ can be larger than P₃; however, the claimedsubject matter is not so limited. Power allocator 208 of base station202 can assign a power level of P₁ during a first time slot, P₂ during asecond time slot, etc. Moreover, a disparate power allocator of theneighboring base station can assign a power level of P₃ during the firsttime slot, P₄ during the second time slot, and so forth. The assignedpower level for a particular time slot can be utilized by a transmitter(e.g., base station 202, one or more mobile device 204-206, . . . ) forcommunicating with a receiver (e.g., one or more mobile devices 204-206,base station 202, . . . ). Following this example, clock 210 can enablebase station 202 to be synchronized with the neighboring base station(and/or any disparate base station(s)). Additionally, another example ofa time-varying power allocation scheme is to enable both base station202 and its neighboring base station choose a power allocation patternwith period 2 by repeating the two power levels chosen by each basestation. Two signal-to-noise ratios (SNRs) can be measured by basestation 202 for effectuating scheduling decisions. Such time divisionpattern reuse can be beneficial for delay sensitive users such as voiceover IP (VOIP) users since the power levels can more rapidly change (ascompared to use of smooth power allocation patterns) without providing auser with a bad SNR for a significant period of time.

According to another illustration, power allocator 208 can use a smoothpower allocation pattern for assigning power rather than a few discretepower levels (e.g., as described in FIGS. 12-13). The smooth powerallocation pattern includes many more power levels into a set ofpossible power levels and enables assigning power levels with smalldifferences to adjacent time intervals, which can enable smooth powervariation over time and more importantly, easier tracking of the SNR.For instance, power allocator 208 can employ a power allocation patternthat can be close to a sinusoidal curve setting forth the power to beassigned as a function of time. The sinusoidal power allocation patterncan have a period of 100 time slots, for example; however, the claimedsubject matter is not so limited as substantially any period or anycurve is contemplated. Meanwhile, the power allocation pattern of aneighboring base station can be phase shifted (e.g., 180 degree shift iftwo power allocation patterns are utilized in a network, 120 degreeshift if three power allocation patterns are utilized in the network, .. . ). Base stations within a network that utilize phase shifted powerallocation patterns can be roughly synchronized (e.g., by respectiveclocks).

According to another example, power allocation patterns utilized bydiffering base stations can be frequency shifted; thus, the sinusoidalcurves of the power allocation patterns can have disparate frequencies.When differing frequencies are employed for the power allocationpatterns, base stations need not be synchronized since over timediffering channel conditions can be observed.

It is to be appreciated that differing power allocation patterns can beemployed by disparate sectors and/or different cells. For instance, withsector-wise reuse, each sector of a cell can utilize a differing powerallocation pattern curve (e.g., respective phase shifted, frequencyshifted, etc. patterns), while the cells in the network can repeat asimilar reuse pattern (e.g., as shown in FIG. 9). Further, for cell-wisereuse, the sectors of a cell can each utilize a common power allocationpattern curve, and each cell can employ a differing power allocationpattern curve as compared to adjacent neighboring cells (e.g., as shownin FIG. 10).

By way of further illustration, the power allocation pattern utilized bybase station 202 can be predetermined and/or adaptively selected.According to an example, each sector and/or cell can be assigned aprefixed power allocation pattern. Pursuant to another illustration, thepower allocation pattern for each sector and/or cell can be adaptiveover time depending upon the load; thus, load information can be sharedbetween sectors and/or cells to adjust mean, frequency, etc. associatedwith power allocation over time. Following this illustration where thereare two cells, one cell can have 10 users and the other cell can have100 users. The average power level for the cell with 10 users can beshifted down in comparison to the average power level for the cell with100 users, for example; however, the claimed subject matter is notlimited to the aforementioned example.

Now turning to FIG. 3, illustrated is an example system 300 thatallocates power levels in a multiple sub-carrier network. It iscontemplated that any number of sub-carriers (e.g., carriers) can besupported by system 300. System 300 includes base station 202 and mobiledevices 204-206 as described above. Base station 202 can further includepower allocator 208 and clock 210. Moreover, base station 202 caninclude carrier selector 302 that can be utilized in conjunction withpower allocator 208 to assign power levels to each of the carriers as afunction of time (e.g., determined by clock 210). Thereafter,transmissions (e.g., users can be selected, . . . ) can be scheduledupon the carriers with the assigned power levels.

According to an illustration, base station 202 can have a maximum powerconstraint. Moreover, carrier selector 302 and power allocator 208 canenable utilizing complementary patterns for power assignment for each ofthe carriers such that the sum of the power can remain constant for allof the carriers supported by base station 202. Carrier selector 302 andpower allocator 208 can utilize discrete power levels and/or smoothpower allocation pattern curves (e.g., sinusoidal curves for eachsub-carrier that can be phase shifted and/or frequency shifted) inconnection with assigning a power level to each of the carriers duringeach time slot. Moreover, the following provides example multiplesub-carrier schemes that can be utilized in connection with system 300.

Turning to FIG. 4, illustrated is an example even power level allocationscheme 400 for a multiple sub-carrier system. According to this example,two transmitters can utilize two sub-carriers; however, it is to beappreciated that the claimed subject matter contemplates utilizing anynumber of transmitters and any number of sub-carriers. By way ofillustration, each of the transmitters can be associated with adisparate sector and/or cell. The hatched bars 402 indicate power usagein sub-carrier 1 for transmitter 1, while the solid bars 404 indicatethe power usage in sub-carrier 2 for transmitter 1. Also, the numberedblocks 406-408 represent the user scheduled at a time slot in eachsub-carrier (e.g., number blocks 406 correspond to sub-carrier 1 andnumber blocks 408 correspond to sub-carrier 2 for transmitter 1). Forinstance, user 1 can be a cell-boundary user and user 2 can be aclose-to-base station user. Additionally, hatched bars 410 representpower usage in sub-carrier 1 for transmitter 2 and solid bars 404represent power usage in sub-carrier 2 for transmitter 2. Numberedblocks 414 indicate the user scheduled at each time upon sub-carrier 1and numbered blocks 416 set forth the user scheduled during each timeupon sub-carrier 2 for transmitter 2 (e.g., user 1′ can be acell-boundary user and user 2′ can be a close-to-base station user).

The power allocation for the two transmitters can be symmetric; thus, if(P₁, P₂) are assigned to the two sub-carriers (represented by f₁ and f₂,respectively) in transmitter 1, (P₂, P₁) will be assigned tosub-carriers in transmitter 2. Moreover, P₁=P₂=P/2, assuming P is atotal available power at each transmitter. By utilizing the even powerlevel allocation scheme 400, users at the boundary of two cells operatebelow 0 dB. Thus, scheme 400 can be favorable for close-to-base stationusers (e.g., user 2), while cell-boundary users can be associated withan SNR below 0 dB. On the other hand, if all power is assigned to one ofthe sub-carriers (not shown) (e.g., and the other sub-carrier isassigned zero power according to such scheme), the boundary user canhave an SNR of hP/N₀, where h is the path loss and N₀ is noise power.Under an interference-limited scenario, the SNR can be larger than 0 dB,which can benefit cell-boundary users. However, by not utilizing one ofthe two sub-carriers, half of the degree of freedom is sacrificed (eventhough power gain can compensate for the loss to improve capacity for aboundary user), which can adversely impact close-to-base station users.Under the aforementioned schemes, neither the cell-boundary users northe close-to-base station users may operate at their optimal operatingpower allocation point due to a tradeoff there between.

With reference to FIG. 5, illustrated is an example time varying powerallocation scheme 500 for a multiple sub-carrier system. Hatched bars502 represent power allocated to sub-carrier 1 and solid bars 504represent power allocated to sub-carrier 2 for transmitter 1. Moreover,blocks 506 identify a user scheduled in sub-carrier 1 at each time slotand blocks 508 identify a user scheduled in sub-carrier 2 at each timeslot. Further, for transmitter 2, hatched bars 510 indicate powerallocated to sub-carrier 1 and solid bars 512 indicate power allocatedto sub-carrier 2, while blocks 514 relate to a user scheduled uponsub-carrier 1 and blocks 516 relate to a user scheduled upon sub-carrier2.

As depicted, power allotted for each of the sub-carriers can change as afunction of time, and thus, the scheme 500 can improve overall spectralefficiency when leveraged by a variety of users (e.g., close-to-basestation users (2, 2′) and cell-boundary users (1, 1′)). Rather thanfixing the power allocation to be the same across time (as in scheme 400of FIG. 4), the scheme 500 can change the power allocation to be either(P/2, P/2) or (P, 0) at differing times (e.g., for transmitter 1).Additionally, transmitter 2 can alternate the power allocation to beeither (P/2, P/2) at differing times. For instance, during a first timeslot shown, transmitter 1 can transmit on sub-carrier 1 to user 1 with apower of P, and during a second time slot can transmit to user 2 with apower level of P/2 on sub-carrier 1 and a power level of P/2 onsub-carrier 2, and so forth. Accordingly, during a subset of the timeslots, sub-carrier 2 can be allocated zero power, and therefore,effectively be turned off. Meanwhile, transmitter 2 can transmit onsub-carrier 2 with a power of P to user 1′ during the first time slotand can transmit to user 2′ on both sub-carriers 1 and 2, each with arespective power of P/2, during the second time slot.

As shown, the transmitters can be symmetric; however, it is contemplatedthat the claimed subject matter is not limited to utilizing symmetricpower allocation patterns. For instance, it is to be appreciated thatthe transmitters can utilize substantially similar periodic powerallocation patterns that have substantially similar periods, yet thepatterns can be offset in phase from one another. Moreover, according tothe illustrated example, user 1 and user 1′ can be cell-boundary usersand user 2 and user 2′ can be close-to-base station users. Moreparticularly, performance for the close-to-base station users can besubstantially similar to a traditional even power allocation scheme(e.g., scheme 400 of FIG. 4). Further, the cell-boundary users canexperience an improved data rate although fewer segments are assigned tosuch users; the improvement in the interference-limited scenario can bedue to increased SNR.

Referring to FIG. 6, illustrated is another example time varying powerallocation scheme 600 for a multiple sub-carrier environment. Hatchedbars 602 represent power usage in sub-carrier 1 and solid bars 604represent power usage in sub-carrier 2 for transmitter 1. Further,blocks 606 indicate an identity of a user scheduled at each time slotfor sub-carrier 1 and blocks 608 indicate an identity of a userscheduled at each time slot for sub-carrier 2 (e.g., where user 1 can bea cell-boundary user and user 2 can be a close-to-base station user).Additionally, hatched bars 610 indicate power usage in sub-carrier 1 andsolid bars 612 indicate power usage in sub-carrier 2 for transmitter 2,with blocks 614-616 providing the corresponding user identitiesscheduled upon the respective sub-carrier (e.g., user 1′ being acell-boundary user and user 2′ being a close-to-base station user). Toimprove spectral efficiency, the scheme 600 can improve the data rate ofclose-to-base station users (e.g., in comparison to the scheme 500 ofFIG. 5). The scheme 600 can improve performance of close-to-base stationusers while maintaining enhanced performance for cell-boundary users incomparison to an even power allocation scheme (e.g., the scheme 400 ofFIG. 4). In particular, the scheme 600 does not shut off one of thesub-carriers (e.g., sub-carrier 2 for transmitter 1, sub-carrier 1 fortransmitter 2, . . . ) during a subset of time slots. Rather, a lowpower level is allotted during such time slots to maintain the SNRimprovement for boundary users that can be significant enough tocompensate for the segment loss (e.g., since the cell-boundary users canbe scheduled upon half of the segments as compared to scheduling in aneven power allocation scheme). Moreover, close-to-base station users(e.g., user 2, user 2′) can be scheduled to the low power levelsegments.

Now referring to FIG. 7, illustrated is an example time varying powerallocation scheme 700 for a single carrier system. Accordingly, powerlevels for the single carrier can be coordinated at different sectors(and/or different cells) during each time slot. Bars 702 represent powerlevels in a first sector during each time slot and bars 704 representpower levels in a second sector during each of the time slots. Moreover,blocks 706 identify a user assigned to each time slot upon the carrierin the first sector and blocks 708 identify a user assigned to each timeslot upon the carrier in the second sector. For example, user 1 and user1′ can be cell-boundary users and user 2 and user 2′ can beclose-to-base station users. Further, the transmitters associated witheach of the sectors can interfere with each other.

The scheme 700 can yield a spectral efficiency improvement similar tothat demonstrated in scheme 500 of FIG. 5. In particular, at a firsttime slot, a cell-boundary user can be assigned a power P in a firstsector, while no assignment can be provided to a user in the secondsector. Next, at a second time slot, a close-to-base station user can beassigned a power P/2 in the first sector and a disparate close-to-basestation user can be assigned a power P/2 in the second sector. Further,at third time slot, a cell-boundary user can be assigned a power P inthe second sector and an assignment can be lacking for the first sector.Moreover, during a fourth time slot, the close-to-base station users canagain be scheduled, and so forth.

Turning to FIG. 8, illustrated is another example time varying powerallocation scheme 800 for a single carrier cellular data network. Thescheme 800 includes bars 802 related to power levels during each timeslot for a first sector and bars 804 related to power levels during eachtime slot for a second sector. Moreover, blocks 806 identify a userassigned to each time slot for the first sector and blocks 808 identifya user assigned to each time slot for the second sector (e.g., user 1and user 1′ can be cell-boundary users, user 2 and user 2′ can beclose-to-base station users, . . . ).

The scheme 800 provides additional segments for close-to-base stationusers (e.g., user 2, user 2′, . . . ) to be scheduled upon. Inparticular, rather than allotting a power level of zero to a firstsector and P to a second sector during a time slot, the first sector canbe assigned a low power level that is greater than zero (e.g., while thesecond sector can be allocated a high power level less than P).Accordingly, a close-to-base station user can utilize the low powerlevel associated with the first sector and a cell-boundary user can beassigned to the high power level corresponding to the second sectorduring this particular time slot. Additionally, during a next time slot,the power levels for each of the sectors can be substantially similar(e.g., middle power level) and close-to-base station users can beassigned to utilize the sub-carrier in each of these sectors.

Referring to FIG. 9, illustrated is an example sector-wise reusemulti-cell deployment 900 in accordance with various aspects of theclaimed subject matter. As depicted, the multi-cell deployment 900 cancomprise multiple cells 902 dispersed over a geographic area to form acommunication network. Each of the cells 902 can include three sectorsas shown; however, it is contemplated that one or more of the cells 902can include fewer than and/or greater than three sectors. Further, it isto be appreciated that the multi-cell deployment 900 can supportmultiple carriers and/or a single carrier.

The sectorized cells 902 can be located in a regular hexagon grid andcan extend beyond the grid depicted (e.g., any number of cells 902 canbe included in the grid, . . . ). For each of the sectors of the cells902, a power variation curve (e.g., P1, P2, P3, . . . ) can be chosen;further, the curves can be reused across all of the sectors. Accordingto the illustrated example, three distinct power variation curves (e.g.,power allocation curves, smooth power allocation pattern curves, . . . )can respectively be allocated to each of the three sectors of each ofthe cells 902; thus, sector 1 can be allocated power variation curve 1(P1), sector 2 can be allocated power variation curve 2 (P2), and sector3 can be allocated power variation curve 3 (P3). Moreover, the samepattern can be reused across all of the cells 902.

FIG. 10 illustrates an example cell-wise reuse deployment 1000 ofmultiple cells for a power allocation reuse scheme. A plurality of cells1002, 1004, 1006 are included within the grid associated with thedeployment 1000. As shown, the cells 1002-1006 include three sectors;however, the claimed subject matter is not limited to utilization ofcells with three sectors. The deployment 1000 can be employed whenleakages from intra-cell sectors are significant. In particular, thedeployment 1000 can use substantially similar power variation curves forsectors inside the same cell and different power variation curves acrossdifferent cells. Thus, according to the depicted example, cells 1002 caninclude three sectors that utilize power variation curve 1 (P1), cells1004 can include three sectors that employ power variation curve 2 (P2),and cells 1006 can include three sectors that use power variation curve3 (P3). Further, each cell 1002 can be adjacent to cell(s) 1004 and/orcell(s) 1006 (and cells 1004 and cells 1006 can similarly be adjacent todiffering types of cells), and therefore, adjacent cells can utilizediffering power variation curves (e.g., a cell 1002 is not directlyadjacent to another cell 1002). It is contemplated, however, that anynumber of differing power variation curves can be employed by differentcells, and thus, the claimed subject matter is not limited to theillustrated example.

Now turning to FIG. 11, illustrated is an example power allocationscheme 1100 for use with differing sectors according to various aspectsof the claimed subject matter. The scheme 1100 includes three powervariation curves 1102, 1104, and 1106 that can be allocated to differingsectors. The power variation curves 1102-1106 can utilize a commoncarrier (e.g., for use in a single carrier system).

By way of example, a cell (e.g., the cell 902 from FIG. 9) can includethree sectors, and each one of the sectors can be assigned a respectiveone of the power variation curves 1102-1106. Moreover, a similar pattern(e.g., assigning power variation curves 1102-1106 to sectors) can berepeated throughout a set of cells. According to another illustration,each sector of a cell can utilize one of the power variation curves(e.g., the power variation curve 1102), and disparate power variationcurves (e.g., the power variation curves 1104, 1106) can be employed bydirectly adjacent cells (e.g., in accordance with the deployment 1000 ofFIG. 10).

The scheme 1100 varies the power allocation in a slot-by-slot basis.Thus, sectors in a network can employ at least some synchronization tocoordinate power of each sector during each time slot. For example, atime division duplexing (TDD) system can support the scheme 1100;however, the claimed subject matter is not so limited. Moreover, thepower variation curve 1102-1106 employed by a particular sector canprovide three states as a function of the power level; hence, a basestation can track variation of the SNRs under each state to makescheduling decisions.

Now referring to FIG. 12, illustrated is an example scheme 1200 thatincludes smooth power variation curves for disparate sectors (and/orcells). The illustrated example includes three power variation curves1202, 1204, 1206; however, it is contemplated that a system can employless than or greater than three power variation curves. As shown, eachof the three power variation curves 1202-1206 can be offset by 120degrees in phase from one another (e.g., if two curves are utilized in adisparate system, the curves can be offset by 180 degrees, if fourcurves are employed then the offset can be 90 degrees, . . . ).According to an example, the power variation curve 1202 can be assignedto all sectors in a cell, and directly neighboring cells can utilize thepower variation curve 1204 and/or the power variation curve 1206.Pursuant to another illustration, a cell can include three sectors, eachof which can employ a corresponding one of the power variation curves1202-1206 (e.g., such a pattern can be repeated across a plurality ofcells).

The scheme 1200 can be employed when a coarser synchronization isavailable over sectors (as compared to the slot-by-slot synchronizationused with the scheme 1100 of FIG. 11). Thus, slot-by-slotsynchronization need not be utilized with the scheme 1200. Moreover, therelative power level can be defined in a linear scale and/or can beoffset. Further, the maximum relative power offset can be scaled by aconstant instead of being fixed to 1.

FIG. 13 illustrates another example power allocation scheme 1300 inaccordance with various aspects of the claimed subject matter. Thescheme 1300 includes three power variation curves 1302, 1304, 1306, eachwith a disparate frequency. By employing the different frequencies forpower variation curves 1302-1306 utilized by disparate sectors, a systemneed not be synchronized. It is contemplated that any frequencies can beutilized for power variation curves 1302-1306. Moreover, it is to beappreciated that fewer than and/or more than three power variationcurves can be utilized in a system.

The following set forth in connection with FIGS. 14-22 providesadditional discussion with regards to various aspects, features,techniques, etc. associated with the claimed subject matter. With theadvent of wideband cellular communications, more and more attention hasbeen drawn to the problem of how to efficiently communicate in amultiple-carrier system. A possible solution to address this problem isto look at the frequency-reuse schemes, which is fairly well studied innarrow-band systems, for example, GSM networks. Specifically, innarrow-band networks, operators typically choose to allocate only partof the total bandwidth to each cell such that the inter-cellinterference can be controlled to be negligible. A scheme whichallocates 1/N of the total bandwidth to each cell is referred to as areuse-N scheme. In narrow-band networks, reuse-N (e.g., where N can bedependent on the geometry of the deployment) can be utilized in amulti-cell deployment since the dynamic range of the inter-cellinterference from neighboring cells due to different locations ofmobiles can make reliable communications difficult.

With CDMA and OFDM technologies, reuse-1 systems can be employed due tothe salient feature of inter-cell interference averaging. Specifically,the inter-cell interference in CDMA and OFDM technologies are averagedover the total bandwidth within a carrier due to the presence ofpseudo-noise signature sequence in CDMA systems and independenttone-hopping in OFDM systems. However, in a reuse-1 deployment, the cellboundary users still suffer from an average SNR below 0 dB. In a typicalhexagon deployment, 30 percent of the users can have an average SNRbelow 0 dB, for example. To satisfy certain fairness constraints betweencell boundary users and other users, the system has to spend a lot ofresource on the cell boundary users, which restricts overall systemperformance. It thus can be desirable to reduce the number of cellboundary users or completely remove the cell boundary, if possible.

Towards this end, the reuse-N schemes can be attractive for widebandsystems. For example, for the regular hexagon deployment, a reuse-3scheme can prevent inter-cell interference from direct neighboring cellsand thus reduce the number of cell boundary users. Of course, for areuse-3 deployment, the system now uses 3 carriers and occupies threetimes the bandwidth as compared to a single-carrier system. Thus, a faircomparison to make here is to compare between systems with the samebandwidth usage. Under certain performance metric, reuse-3 canoutperform reuse-1. However, if networks with mainly elastic trafficsources are considered, for example, delay-insensitive data users,reuse-3 may not be the best choice due to its conservativeness inbandwidth reuse. Each cell only uses ⅓ of the total bandwidth to achievea power gain for the cell boundary users and a tradeoff from bandwidthto power is usually not beneficial. Towards this end, a more flexible“frequency-reuse” scheme, which is referred to as a Flex-Band scheme,can be utilized.

In the Flex-Band proposal, all carriers can be used in all cells. Thus,from frequency-reuse point of view, it is a reuse-1 approach. However,each carrier is allowed to choose a different power level in the samecell. Different cells use a different power-reuse scheme within thecell. Apparently, the Flex-Band proposal is essentially a fractionalpower reuse scheme and both the simple frequency reuse-1 scheme andreuse-3 scheme are special cases of it. For brevity of notation, thefrequency reuse-1 scheme can be referred to as the reuse-1 scheme andthe frequency reuse-N scheme can be referred to as reuse-N scheme.

In cellular networks, the spectral efficiency can be defined as the datacapacity normalized by bandwidth. Moreover, the spectral efficiency canbe an important system performance metric to compare between differenttechnologies. Specifically, the spectral efficiency is the cell overallthroughput normalized by bandwidth when certain number of data users aredropped uniformly in cells. Further, the cell throughput is measuredwhen a certain fairness criterion is enforced among different users inthe system (e.g., the system can not maximize its throughput by puttingall its resource to close-to-base station users).

The following analyzes whether it is beneficial to adopt a fractionalpower reuse scheme in a multi-carrier downlink, from a spectralefficiency point of view. Specifically, the capacity region of thesystem under a fractional power reuse scheme can be studied and comparedto the capacity region under the even-power-allocation scheme. Forinstance, the following can be determined:

(1) In a single-cell TDMA scheme where a user is scheduled in each timeslot with a fixed power constraint, a fractional power reuse scheme canyield a better capacity region as compared to the reuse-1 scheme.However, the improvement can be slim and if more than one user that canbe scheduled is used in each carrier, the same improvement can beachieved even with the reuse-1 scheme.

(2) In a multi-cell system, the capacity region can be improved byfractional power reuse. This improvement can not be achieved by relaxingthe one-user-per-slot policy and this shows that fractional power reusecan enable achieving the capacity region in a multi-cell multi-usersystem.

(3) The capacity region of a multi-cell system can be further improvedby introducing time variation in the fractional power reuse scheme,which is an opportunistic power reuse scheme and is also referred to thebreathing-cell scheme. In this scheme, each cell can vary its transmitpower with a different frequency and/or phase, or equivalently saying,with a different power allocation pattern. The total number of powerallocation patterns can be limited and can be reused over the entirenetwork. Each cell can schedule cell boundary users when the channelcondition (e.g., depending on its current transmit power and inter-cellinterference) is good and can schedule close-to-base station users whenthe channel is bad.

A wideband cellular downlink can be considered with a given number ofcarriers. Communications scheduled in different carriers do notinterfere with each other while simultaneous communications in samecarriers in different cells create inter-cell interference. This is alsoreferred to as the co-channel interference. Theoretically, if we assumeperfect backhaul between the base stations, one can apply CostaPre-coding at each base station to remove the co-channel interference,if the concurrent communications in neighboring cells can be known in anon-causal way. However, such a scheme may not be practical in realitydue to the following two difficulties: (i) Costa pre-coding uses perfectknowledge of the channel side information at the base station; (ii) thisscheme leverages symbol-level global system synchronization.Additionally, the complexity of such a scheme is very high. Thus, it isnot assumed that such schemes are to be used at the base stations. Eachbase station can treat the inter-cell interference as a pure additive tothe noise which can not be taken advantage of.

For simplicity, time can be assumed to be slotted. In each time slot,one user per carrier per cell can be allowed to transmit (e.g., a TDMAscheme). TDMA downlink has been adopted into many systems includingIS-856 (EV-DO) systems, for example. With this assumption, intra-cellinterference can be mitigated and thus the effect of power reuse schemeson the inter-cell interference can be reviewed. It is to be appreciatedthat although a TDMA approach is described herein, more than one usercan be allowed to be scheduled within the same slot using an orthogonalsystem resource, which is possible in an OFDM-based network.

Users can be considered to be stationary (e.g., the channel is AWGNbetween the user and the base station or the channel varies in a slowertime scale as compared to the communication time scale). When a user iis assigned the slot t, it can transmit at a rate of

${C_{i}(t)} = {\log_{2}\left( {1 + \frac{h_{i}{P_{i}(t)}}{N_{0}}} \right)}$bits per second, where h_(i) is the channel gain between user i and itsserving base station and P_(i)(t) is its transmit power at time t. N_(o)is the noise power density (e.g., the following assigned N_(o)=1).Further, a power budget at the base station (e.g., the average powerused per carrier) can be bounded by P_(m).

A determination can be made as to how to allocate power levels todifferent carriers in different cells to maximize the system capacity.In a data network, the spectral efficiency (bits per second per Hertz)can be a useful capacity metric to compare different networks, where allusers are assumed to be infinite-backlogged. However, spectralefficiency is usually defined associated with a given fairness criterionbetween users within the network and is thus hard to characterize inclosed-form expressions. Thus, the following considers the capacityregion instead of the spectral efficiency. The spectral efficiency undera fairness constraint can be viewed as an operating point within thecapacity region. By considering the capacity region, the impact ofdifferent schemes under different fairness constraints can be evaluated.According to an example, the capacity region for a two-user system canbe considered, where one user is chosen to be a cell-boundary user whilethe other one is close to the base station. This model can be a goodsimplification of a loaded system where multiple users are droppeduniformly in each cell.

Each mobile can be a wideband mobile (e.g., it can be scheduled in partof or all the carriers). The system scheduler can choose which users totransmit on each carrier without worrying about whether or not a mobilecan transmit/receive on a particular carrier.

Single cell scenario: When only a single cell and a single user areconsidered, the problem considered degrades to a point-to-pointcommunication problem over parallel channels. In such a scenario, due tothe concavity of the Shannon capacity formula, it is optimal to allocateyour power evenly across the parallel channels and make full use of theavailable degrees of freedom (e.g., there is no benefit to vary thepower allocation across carriers or time). However, in a multi-userscenario, such observation is not true anymore. In other words, benefitcan be obtained from varying power across carrier or time to do betterthan the even-power-allocation scheme. For convenience, in thefollowing, the even-power-allocation scheme is referred to as a simpleReuse-1 scheme.

Next, the capacity region for two users under a two carrier system witha fixed power allocation scheme can be evaluated, where each carrierchooses a time-invariant power level.

Capacity region under fixed power allocation scheme: In this section, atwo-user single-cell system with two carriers is evaluated. The powervector allocated to the two carriers is (P₁, P₂). The main result ofthis section is summarized in the following theorem.

Theorem 1: Assume the path-loss gains for the two users in the systemare h₁, h₂ and satisfy h₂≧h₁. The capacity region under a fixed powerallocation scheme (P₁, P₂) (P₂≧P₁) is the convex hull of four capacityvectors (0, 0), (R₁, 0), (0, R₂), and (R′₁, R′₂), where R₁, R₂, R′₁, R′₂are defined below.R ₁=log₂(1+h ₁ P ₁)+log₂(1+h ₁ P ₂);  (1)R ₂=log₂(1+h ₂ P ₁)+log₂(1+h ₂ P ₂);  (2)R′ ₁=log₂(1+h ₁ P ₂);  (3)R′ ₂=log₂(1+h ₂ P ₁).  (4)

Remark: The capacity region illustrated in FIG. 14 is a polygon withvertexes given by (0, 0), (R₁, 0), (0, R₂), and (R′₁, R′₂). R_(i) (i=1,2) is the capacity of user i when both carriers schedule user i only allthe time. Since h₂>h₁, user 1 can be referred to as the bad user anduser 2 as the good user. Similarly, carrier 1 can be referred to as thegood carrier and carrier 2 as the bad carrier. (R′₁, R′₂) is thecapacity tuple when the good user is scheduled on a bad carrier only andthe bad user is scheduled on the good carrier only. FIG. 14 shows anexample of such a region.

This region is essentially a convolution of the capacity regions for thetwo carriers. Specifically, the region consists of all rate tuples whichcan be expressed in the form of the summations of two rate tuples, eachbelonging to the capacity region of a carrier. Such sum is also referredto as the Minkawski sum of two convex regions.

Proof: The achievability can be simple. By scheduling only user 1 tocarrier 2 (e.g., the bad user uses all the resource of the goodcarrier), and by varying the fraction of time that user 1 is scheduledin carrier 2, points on the straight line with end points (R₁, 0) and(R′₁, R′₂) can be achieved. On the other hand, by scheduling only user 2to carrier 1 and varying the fraction of time that user 2 is scheduledwithin carrier 2, the straight line between (0, R₂) and (R′₁, R′₂) canbe achieved.

FIG. 15 illustrates the converse via a graphical approach. In FIG. 15,straight line I denotes the boundary of the capacity region for carrier1, II denotes the boundary of the capacity region for carrier 2. Anobservation that can be made here is if the two capacity regions for thetwo carriers are compared, such that the bad user can be improved by alarger factor by scheduling it on the good carrier. This is again due tothe concavity of the capacity. Thus, line I is steeper as compared toline II.

The capacity region of the two-carrier system is then the set of ratetuples which can be written as the summation of a rate tuple within thecapacity region of carrier 1 and a rate tuple within the capacity regionof carrier 2. For simplicity, the capacity region can be equal to I+II.Apparently, the capacity region has to be bounded by both I+II′ andI′+II, where I′ and II′ are also shown in FIG. 15. Specifically, line I′is parallel to II and intersects the R₂ axis at the same end point as I.II′ is parallel to I and intersects the R₁ axis at the same end point asII. Similarly, straight line III is parallel to straight lines I′ and IIand intersects the R₂ axis at (0, R₂) while straight line IV is parallelto straight lines I and II′ and intersects the R₁ axis at (R₁, 0).

Further, it can be shown that III=I′+II and IV=I+II′. To see thatIII=I′+II (the other proof can be similar), it suffices to see that thesummation of any point (x₁, y₁) on I′ and any point (x₂, y₂) on II hasto reside on III. This is true since I′ and II have the same slope andthus the two points can be represented by the following:y ₁ =−sx ₁ +c ₁;y ₂ =−sx ₂ +c ₂,where s is the common slope and c₁, c₂ are two constants. It can be seenthat y₁+y₂=−s(x₁+x₂)+c₁+c₂, for any choice of (x₁, y₁)εI′ and (x₂,y₂)εII. Next, the straight liney=−sx+c ₁ +c ₂,  (5)can be shown to coincide with III. It suffices to show that (0, R₂)satisfy (5), e.g., R₂=c₁+c₂. This is trivial since c₁ and c₂ are therate that user 2 can achieve within carrier 1 and 2 when all resourcesare allocated to it while R₂ is maximum rate user 2 can get in bothcarriers. The theorem follows.

A by-product of the proof above is that the optimal scheduling policy ofa multi-carrier system, from a capacity point of view, can bedetermined.

Corollary 1: To achieve any point on boundary of the capacity region ofa fixed power-allocation two-carrier system, at least one of thefollowings must be true (1) the good user is only scheduled in the badcarrier; or (2) the bad user is only scheduled in the good carrier.

Proof: Assume that there is a point on the boundary of the capacityregion shown above which can be achieved by a scheme without satisfyingcondition (1) or (2). Equivalently saying, a scheme where both users arescheduled to both carriers which actually achieves a rate tuple on thecapacity boundary can be utilized. Assuming α_(ij)=(i,j=1, 2) to be thetime fraction that user i is scheduled on carrier j. Thus,α₁₁+α₂₁=α₁₂+α₂₂=1. The rate tuple achieved by this scheme is thus(α₁₁C₁₁+α₁₂C₁₂,α₂₁C₂₁+α₂₂C₂₂), where C_(ij) is a capacity of user i whenscheduled in carrier j, e.g., C_(ij)=log₂(1+h_(i)P_(j)). Thus, anobservation that can be made is that:

$\begin{matrix}{{\frac{C_{12}}{C_{11}} > \frac{C_{22}}{C_{21}}},} & (6)\end{matrix}$e.g., the benefit of scheduling the bad user in the good carrier isdominating the benefit of scheduling the good user there.

It can be shown that this rate tuple cannot be on the boundary if bothα₁₁ and α₂₂ are non-zero, e.g., there exists an achievable rate tuplewhich is strictly larger than this one component wisely. To see this,the rate tuple achieved under time fraction β_(ij) can be considered,where β_(ij) is again the time fraction that user i is scheduled oncarrier j. Moreover, β_(ij) can be chosen as follows:β₁₁=α₁₁−η;β₁₂=α₁₂+ε;β₂₁=α₂₁+η;β₂₂=α₂₂−ε,where η and ε are small positive numbers which satisfy

$\frac{C_{22}}{C_{21}} < \frac{\eta}{ɛ} < {\frac{C_{12}}{C_{11}}.}$Since α's are positive, small enough η and ε can be identified such thatthe β's are positive as well.

The rate tuple achieved by this scheme can be seen to be(α₁₁C₁₁+α₁₂C₁₂−ηC₁₁+εC₁₂,α₂₁C₂₁+α₂₂C₂₂+ηC₂₁−εC₂₂) which is larger thanthe rate tuple under α_(ij) component wisely. Thus, there exists acontradiction.

Remarks: This corollary gives a general guideline for schedulingpolicies in a multi-carrier system. As shown below, the same rule isalso true in a multi-cell system where inter-cell interference exists.

Comparison to the reuse-1 scheme: The capacity region under a fixedpower allocation scheme was evaluated above. Now, it can be determinedwhether or not it is optimal to allocate power evenly across thecarriers, by comparing the capacity region under a general (P₁, P₂)allocation to the one under reuse-1 scheme.

Apparently, for the two extreme points (R₁, 0) and (0, R₂), to deviatefrom the simple reuse-1 scheme is suboptimal as seen in the single usercase. But it is not yet proved if the capacity region under a general(P₁, P₂) scheme is a subset of the capacity region under theeven-power-allocation scheme. By choosing (P₁, P₂) carefully, beneficialresults can be obtained in comparison to the even-power-allocationscheme in some part of the capacity region.

Lemma 1: Consider a two-user two-carrier single-cell system with h₁<h₂.There exist a power allocation scheme (P₁, P₂) such that the capacityregion under (P₁, P₂) is not a subset of the capacity region underReuse-1 scheme.

Proof: To see this, the point (R′₁, R′₂) as defined in (3) and (4) isconsidered. Since the capacity region under Reuse-1 is a linear regionunder the system assumption, (R′₁, R′₂) is a candidate to consider herebecause it is the vertex of the polygon which may not be included in theReuse-1 capacity region.

The capacity region can be written as

$\left\{ {\left( {R_{1},R_{2}} \right):{{\frac{R_{1}}{2{\log_{2}\left( {1 + {h_{1}P_{m}}} \right)}} + \frac{R_{2}}{2{\log_{2}\left( {1 + {h_{2}P_{m}}} \right)}}} \leq 1}} \right\}.$Thus, it suffices to show that there exists an αε(0, 1] such that (P₁,P₂)=((1−α)P_(m), (1+α)P_(m)) and

${\frac{\log_{2}\left( {1 + {h_{1}P_{2}}} \right)}{2\log\; 2\left( {1 + {h_{1}P_{m}}} \right)} + \frac{\log_{2}\left( {1 + {h_{2}P_{1}}} \right)}{2{\log_{2}\left( {1 + {h_{2}P_{m}}} \right)}}} > 1.$The left-hand-side of the inequality above can be defined as g(α). Thus,g(0)=1.  (7)

Further, the first-order derivative of g(α) is

${g^{\prime}(a)} = {{\frac{1}{\log_{2}\left( {1 + {h_{1}P_{m}}} \right)}\frac{1}{1 + \frac{\alpha\; h_{1}P_{m}}{1 + {h_{1}P_{m}}}}\frac{h_{1}P_{m}}{1 + {h_{1}P_{m}}}} - {\frac{1}{\log_{2}\left( {1 + {h_{2}P_{m}}} \right)}\frac{1}{1 - \frac{\alpha\; h_{2}P_{m}}{1 + {h_{2}P_{m}}}}{\frac{h_{2}P_{m}}{1 + {h_{2}P_{m}}}.}}}$Further,g′(0)>0,  (8)if h₁<h₂. This can be true because

${g^{\prime}(0)} = {{\frac{1}{\log_{2}\left( {1 + {h_{1}P_{m}}} \right)}\frac{h_{1}P_{m}}{1 + {h_{1}P_{m}}}} - {\frac{1}{\log_{2}\left( {1 + {h_{2}P_{m}}} \right)}\frac{h_{2}P_{m}}{1 + {h_{2}P_{m}}}}}$g^(′)(0) = f(h₁P_(m)) − f(h₂P_(m))where f(.) can be defined as

${f(x)} = {\frac{1}{\log_{2}\left( {1 + x} \right)}\frac{x}{1 + x}}$and can be shown to be a monotone decrease function for x>0. The lemmafollows from (7) and (8).

From here, if (P₁, P₂) is chosen appropriately, better results can beobtained than the reuse-1 scheme for certain choice of utility function,or equivalently, fairness criterion. On the other hand, an uneven powerallocation leads to a sub-optimal performance when the operating pointshifts to the end points where most system resource is allocated to oneof the users. Such properties are depicted in FIG. 16.

Capacity region under opportunistic power allocation: The capacityregion for a single-cell two-carrier system can be considered, byintroducing time-varying power allocation across time. Specifically, ineach time slot, the scheduler of the system can determine both (1) whichuser to transmit on each carrier, and (2) which power level to use oneach carrier under the average power constraint.

The benefit of allowing time-varying power allocation is apparent fromFIG. 16. As illustrated, curve 1602 is a capacity region under reuse-1,curve 1604 is a capacity region under (P₁, P₂), and curve 1606 is acapacity region under time-sharing. As shown in FIG. 16, a naive lowerbound to the true capacity region can be obtained by performingtime-sharing between the two end-points of the reuse-1 scheme and thebetter-performance point (R′₁, R′₂) under any power allocation scheme.This yields a capacity-region curve consist of two straight lines whichcan outperform reuse-1 at all points. The capacity region can further beoptimized by looking at all possible (P₁, P₂) allocations. However, thisscheme is not necessarily optimal. Next, it can be determined whetherfurther optimization can be obtained and/or what is the optimal user andpower scheduling policy as shown in the next theorem.

Theorem 2: Assume the path-loss gains for the two users in the systemare h₁, h₂. The capacity region of the single-cell two-carrier system isthe convex hull of following rate tuples {(2αlog₂(1+h₁P₁),2(1−α)log₂(1+h₂P₂)):0≦α≦1,αP₁+(1−α)P₂=P_(m)}.

Remarks: In the expression above, α is the usual time-sharing parameter,which represents the time fraction that the system is scheduling one ofthe users. P₁ and P₂ can be viewed as the power-sharing parameters. Thistheorem yield that to achieve any point on the boundary of the capacityregion under the one-user-per-slot-per-carrier constraint, the optimalstrategy utilizes a time/power sharing strategy instead of the simpletime-sharing strategy, which yields the straight-line region underreuse-1. In this strategy, the system picks different power levelsaccordingly when it schedules different users. After a power level ispicked, the system sticks to it when the same user is scheduled.

Proof: Achievability is trivial. User 1 can be scheduled in α of thetotal segments over both carriers and use power P₁ to transmit. User 2is scheduled 1−α of the total segments using P₂.

For the converse, it can be argued that any rate tuple which is out ofcapacity region defined above may not be achieved. For any schedulingpolicy, it can be assumed that user 1 gets a fraction of the totalsegments with average power P₁ and user 2 gets the rest of the segmentswith average transmit power P₂. Due to the concavity of the capacity,the rate that user 1 obtained under this scheduling policy is upperbounded by 2α log₂(1+h₁P₁) which is achieved by spreading the powerevenly across the segments (or degrees of freedom) assigned to thatuser. A similar argument can be made with regarding to user 2.

Another observation that can be made is that in the proof of Theorem 2,the fact that there are two carriers can be irrelevant. Such a schemecan be easily extend to the single-carrier system, where flexibletime/power sharing can be applied to achieve a better capacity region ascompared to the simple reuse-1 scheme. A comparison between the capacityregion under this scheme and the reuse-1 scheme is shown in FIG. 17.FIG. 17 illustrates an example comparison of capacity regions undersimple reuse-1, general time/power sharing and superposition. Asdepicted, 1702 represents a capacity region under reuse-1, 1704 depictsa capacity region under opportunistic power allocation, and 1706represents a capacity region under super-position.

The benefit of flexible time/power sharing against the simple reuse-1scheme can decrease as the difference between two users gets smaller.Further, if the one-user-per-slot constraint is removed to allowscheduling multiple users, then the information-theoretic capacityregion is achieved by super-position coding and decoding, which can bebetter than the capacity region under time/power sharing.

To allow power to vary over time arbitrarily may not be desirable incellular networks since it will cause fluctuation in inter-cellinterference and thus make channel quality tracking difficult. On theother hand, superposition coding also adds complexity to the system.Accordingly, alternative ways to achieve the capacity region beyond thelinear Reuse-1 region without applying either time/power sharing orsuperposition coding can be leveraged.

A possibility to improve the spectral efficiency is to introduce themulti-carrier system. To have a two-carrier system can achieve some ratetuples outside the linear region, by choosing power levels andscheduling policies carefully. Now consider a system with infinitenumber of carriers. In this case, the capacity region (normalized by thenumber of carriers) can be the same as the single-carrier capacityregion under flexible time/power sharing, since power can be assigned tocarriers in a similar way to that proposed in the time/power sharingscheme in the time domain.

When considering a finite number of carriers, a quantization error canresult if time-varying power allocation is not allowed. Specifically,the percentage of degrees of freedom using a specific power level is notof infinite precision any more. Thus, the capacity region achievablewith a finite number of carriers will be a subset of the single-carriercapacity region under time/power sharing.

In an orthogonal system, for example, an OFDM system, the super linearcapacity region can be achieved even with a single carrier sincemultiple sub-carrier tones can be included within a carrier. If morethan one user is allowed to schedule in the same time slot within thesame carrier, then more energy can be used on some of the tones wherethe bad user can be scheduled while the good user can be scheduled atthe rest of the tones. Additionally, a single cell scenario can besimilar to a multi-carrier system under the one user per carrier perslot constraint.

Two-cell Scenario: A two-cell scenario can be evaluated. Similar to thesingle-cell scenario, the capacity region for a multi-carrier system canbe reviewed and then the capacity region under an opportunistic powerallocation scheme can be analyzed, which can be applied to singlecarrier systems. For a two-cell case, the definition of capacity regioncan be slightly different from the capacity region described above. Forinstance, the following provides assumptions and defines capacity regionin connection with the two-cell scenario.

Definitions and assumptions: The capacity region described for thetwo-cell scenario can be the capacity region for users in one of thecells. The cell of interest can be referred to as the primary cell andthe other cell can be referred to as the interfering cell or simply theinterferer. Clearly, the capacity region of the primary cell depends onthe transmitting power in the interferer cell. The interferer can beassumed to be blasting at the maximum allowed power in its carriers.This assumption is valid in a loaded system where the spectralefficiency is calculated.

Another factor which will affect the capacity region is the powerallocation in the carriers of the interferer cell. Towards this end,another assumption can relate to the symmetry between these two cells.Specifically, assume L carriers in each cell and assume that the primarycall assign power vector P=(P₁, P₂, . . . , P_(L)) to the L carriers. Bythe symmetry assumption, the power allocation can be constrained in theinterferer cell to be a permutation of P. Further, assuming π_(ij) to bethe fraction of carriers where the primary cell assigns power levelP_(i) and the interferer assigns P_(j), then π_(ij)=π_(ji).

As an example, consider the case where two carriers exist in each cell.If (P₁, P₂) is used in the primary, then the symmetry assumptionconstrains the power allocation to the two carriers in the interferer tobe either (P₁, P₂) or (P₂, P₁). Any other power allocations (e.g., powerallocations using any other power levels) in the interferer can beexcluded.

Due the presence of the interferer, the channel quality from a mobile toboth cells can affect the performance for a user. For notationalconvenience, η_(i) to be the path loss ratio of user i, e.g.,

${\eta_{i} = \frac{h_{i}^{(2)}}{h_{i}^{(1)}}},$where h_(i) ^((k)) represents the path loss gain between user i and cellk. After introducing η_(i), the super index for the h's and a user'schannel need not be used and can be represented by the channel gainh_(i) and the path loss ratio η_(i).

In general, h_(i) and η_(i) are not necessarily fully correlated. Ifthere are two mobiles, for example, the one with better h_(i) can have alarger path loss ratio. To reduce the complexity of the problem, it canbe assumed that η_(i) and h_(i) are fully correlated when multiple usersare considered, e.g., if h₂≧h₁, then η₂≦η₁. With this assumption, forusers with better channel quality, they see less interference from theinterferer too and thus the path loss h_(i) can distinguish between a“good” user and a “bad” user.

System capacity with two carriers under fixed power allocation: First,two carriers in each cell in the system can be considered. Due toexistence of the interferer, an even-power-allocation scheme is notguaranteed to be optimal even for a single user. For example, consider auser in the cell boundary, e.g., η≈1. In this case, aneven-power-allocation leads to approximately zero SNR and further limitthe sum rate for this user, if the system allocates all the resources tohim, by 2 bits per second, according to (14). However, all the power isassigned to one of the carriers, e.g., choose (P₁, P₂)=(2 P_(m), 0),this user will lose half of the degrees of freedom and obtain a powergain on the carrier in use. Due to the concavity of capacityformulation, when the interference does not change, it is beneficial touse more degrees of freedom rather than focusing the power on part ofthe bandwidth. However, at the presence of an interferer, it is possiblethat the power gain can dominate the loss in degrees of freedom.Specifically, using the formulation in (14), the SNR under a (2 P_(m),0) allocation is h₂P₂. In an interference limited scenario, we haveh₂P₂>>1. Apparently, in this case, a capacity gain for certain users canbe obtained by allowing power allocation to deviate from theeven-power-allocation scheme. In particular, the maximum capacity of asingle user in the two-cell system can be evaluated as follows.

Single user capacity with two carriers: The following problem can beanalyzed: what is the optimal power allocation scheme in the presence ofa cooperative interferer for a given user? The following lemma answersthis question.

Lemma 2: The optimal power allocation scheme for a mobile parameterizedby channel gain h and path-loss ratio η (the subscript can be removed inthis lemma since all resources can be scheduled to a single user in theprimary cell) is either a reuse-1 or a reuse-2 scheme, e.g., (P_(m),P_(m)) or (2P_(m), 0).

Proof: To see this, the sum capacity (over the two carriers) of a userunder a power allocation scheme (P_(m)+x, P_(m)−x) can be represented asa function of x, which is the amount of power chosen to deviate from theeven-allocation method:

${C(x)} = {{\log_{2}\left( {1 + \frac{h\left( {P_{m} + x} \right)}{1 + {\eta\;{h\left( {P_{m} - x} \right)}}}} \right)} + {{\log_{2}\left( {1 + \frac{h\left( {P_{m} - x} \right)}{1 + {\eta\;{h\left( {P_{m} + x} \right)}}}} \right)}.}}$

C(x) can be maximized for xε[−P_(m), P_(m)] when x=0, x=P_(m), orx=−P_(m). Since C(x)=C(−x), it suffices to show that C(x) is eithermonotonely decreasing or increasing within the interval xε[0, P_(m)].

To see this, the first-order derivative of C(x) with respect to x can beevaluated such that

$\begin{matrix}{{{C^{\prime}(x)} = {\frac{1}{\ln(2)}\left\{ {\frac{1}{x + z_{1}} - \frac{1}{z_{1} - x} - \frac{1}{x + z_{2}} + \frac{1}{z_{2} - x}} \right\}}},} & (9)\end{matrix}$where the poles z₁ and z₂ are defined below

$\begin{matrix}{{z_{1} = {P_{m} + \frac{1 + {2\eta\;{hP}_{m}}}{\left( {1 - \eta} \right)h}}};} & (10) \\{z_{2} = {P_{m} + {\frac{1}{\eta\; h}.}}} & (11)\end{matrix}$

It can be determined that z₁, z₂>P_(m). Given xε[−P_(m), P_(m)], thefour terms (without sign) in (9) are all positive. Further, if z₁>z₂,then C′(x)>0 for all xε[0, P_(m)] while if z₁≦z₂, then C′(x)<0.

The condition for z1>z2 in the proof above is

$\begin{matrix}{{hP}_{m} > {\frac{1 - {2\;\eta}}{2\;\eta^{2}}.}} & (12)\end{matrix}$In other words, for users satisfying (12), the optimal power allocationscheme is reuse 2. On the other hand, for mobiles that cannot satisfy(12), the optimal power allocation scheme is reuse 1. There are twoobservations that can be derived from this condition: (1) Given a powerconstraint P_(m) at the base station, mobiles with worse path loss ratioare more likely to benefit from a reuse-2 allocation; and (2) Given amobile constrained by h and η, it is more likely for this mobile tobenefit from a reuse-2 allocation in a base station with higher powerconstraint. Simply put, reuse-2 allocation is more favorable for aninterference-limited deployment with a lot of cell-boundary mobiles.

Two user capacity region: As before, the capacity region of two usersunder a given power allocation vector (P₁, P₂) in the primary cell canbe considered. As utilized above, a power allocation can be (P₁, P₂) or(P₂, P₁) in the interferer cell. (P₁, P₂) in the interferer may not bean interesting scenario since in this case, in the interference-limiteddeployment, the performance can be quite similar to the simple reuse 1scheme. Thus, the capacity region under power allocation (P₁, P₂) at theprimary and (P₂, P₁) at the interferer can be evaluated.

Theorem 3: Assume the path-loss gains for the two users in the primarycell are h₁, h₂ and satisfy h₂≧h₁. Assume the path loss ratio η₁, η₂satisfy η₁≧η₂. The capacity region under a fixed power allocation scheme(P₁, P₂) (P₂≧P₁) is the convex hull of four capacity vectors (0, 0),(R₁, 0), (0, R₂), and (R′₁, R′₂), where R₁, R₂, R′₁, and R′₂ are definedbelow.

$\begin{matrix}{{R_{1} = {{\log_{2}\left( {1 + \frac{h_{1}P_{1}}{1 + {\eta_{1}h_{1}P_{2}}}} \right)} + {\log_{2}\left( {1 + \frac{h_{1}P_{2}}{1 + {\eta_{1}h_{1}P_{1}}}} \right)}}};} & (13) \\{{R_{2} = {{\log_{2}\left( {1 + \frac{h_{2}P_{1}}{1 + {\eta_{2}h_{2}P_{2}}}} \right)} + {\log_{2}\left( {1 + \frac{h_{2}P_{2}}{1 + {\eta_{2}h_{2}P_{1}}}} \right)}}};} & (14) \\{{R_{1}^{\prime} = {\log_{2}\left( {1 + \frac{h_{1}P_{2}}{1 + {\eta_{1}h_{1}P_{1}}}} \right)}};} & (15) \\{R_{2}^{\prime} = {{\log_{2}\left( {1 + \frac{h_{2}P_{1}}{1 + {\eta_{2}h_{2}P_{2}}}} \right)}.}} & (16)\end{matrix}$

Proof: The proof is similar to the proof to Theorem 1.

Remarks: R_(i) (i=1, 2) can be the capacity when both carriers areassigned to user i and (R′₁, R′₂) can be the rate tuple when the gooduser is scheduled to the bad carrier and the bad user is scheduled tothe good carrier. The capacity region of an arbitrary power allocationmethod can be compared to the capacity regions under reuse 1 and reuse 2scheme. For simplicity, the case where a good user and a bad usercoexist in the primary cell can be evaluated. However, it should benoted that the definition of good and bad is different than the onesused in the single cell case. In the single cell case, there is no clearconstraint to quantize how good a user is and the words good and badcome from the relative channel quality comparison between the two users.Here, a bad user can be a user with an h and q such that (12) issatisfied while a good user can be a user such that (12) is notsatisfied. FIG. 18 illustrates example capacity regions under such anassumption.

Referring to FIG. 18, illustrated is an example of capacity regions fora two-user two-carrier two-cell system under reuse-1, reuse-2 and a (P₁,P₂) allocation. At 1802, a reuse-1 capacity region is illustrated. At1804, a reuse-2 capacity region is shown. Further, at 1806, a (P₁, P₂)capacity region is depicted. Moreover, 1808 represents an achievabilityregions under all power allocation schemes. As shown in FIG. 18, thegood user's rate is maximized in a reuse-1 scheme while the bad user'srate is maximized in reuse-2 scheme. For a general (P₁, P₂) allocation,the capacity region is again a convex region characterized by Theorem 3.

Further, the set of achievable rate tuples under any power allocationscheme can be analyzed. This achievable region can be the union of thecapacity regions under all power allocation schemes and is also shown at1808. For any rate tuple within this achievable region, a powerallocation scheme and a scheduling policy to achieve this rate tuple canbe determined. However, it is to be appreciated that this region is notnecessarily a convex region.

Opportunistic power allocation: Schemes to improve upon the rate regionsachieved in FIG. 18 can leverage introducing time-varying powerallocation scheme. Due to the non-convexity of the rate region by thefixed power allocation scheme, the region can be improved bytime-sharing between different power allocation schemes. An example isto time-share with reuse-1 and reuse-2, which can effectuate achieving alinear region connecting the point (R₁, 0) and (0, R′₂). Further,similar to the single cell case, after introducing time-variation, thereis not much difference between a single-carrier system and amulti-carrier system, from a spectral efficiency point of view. Thus,the capacity region under an average power constraint when a corporativeinterferer exists can be evaluated as described below.

A single-carrier two-cell can be utilized according to an example. Ateach time slot, the scheduler can pick one user to transmit and a powerlevel to transmit under an average power constraint. Again, to maximizethe throughput in the primary cell, the interference cell can shut downcompletely. Here, again a symmetry assumption can be utilized.Specifically, both cells can be assumed to have to choose from the samepower alphabet. A power alphabet is a set of discrete power levels thata cell is allowed to choose from at a given time slot. Assuming thepower alphabet is P₁, P₂, . . . , P_(L), we define a matrix π={π_(ij)},1≦i,j≦L, where π_(ij) represents the time fraction that the primary cellchooses power level P_(i) while the interferer chooses P_(j). Assumingsymmetry can enforce that π_(ij)=π_(ji).

Single user capacity under opportunistic power allocation: The capacityfor a single user in the primary cell can be reviewed. When theinterferer does not exist, or the interferer chooses aeven-power-allocation scheme, e.g., interferer is incorporative, thestrategy for the primary cell is also to use an even-power-allocationscheme. However, when a corporative interferer exists, the problem isnot well understood even for a single user. The study of the single usercapacity will also lead to the end-points in the capacity region whenmore than one user exist in the primary cell and give insight into themultiuser problem.

The single-user capacity problem can be formulated as below:

$\begin{matrix}{\max_{P,\pi}{\sum\limits_{ij}{\pi_{ij}C_{ij}}}} & (17) \\{{{s.t.{\underset{\mspace{56mu}{ij}}{\overset{\;}{\mspace{45mu}\sum}}\pi_{ij}}} = 1};} & (18) \\{{{\underset{\mspace{101mu}{ij}}{\overset{\;}{\mspace{76mu}\sum}}{\pi_{ij}P_{i}}} = P_{m}};} & (19) \\{\mspace{79mu}{{0 \leq \pi_{ij} \leq 1},{\forall i},{j;}}} & (20) \\{\mspace{79mu}{{\pi_{ij} = \pi_{ji}},}} & (21)\end{matrix}$where C_(ij) is the capacity of the user, (characterized by h and η),when the primary cell chooses P_(i) and the interferer chooses P_(j).For simplicity, again the AWGN Shannon capacity formula can be utilizedand

$\begin{matrix}{C_{ij} = {{\log_{2}\left( {1 + \frac{{hP}_{i}}{1 + {\eta\; h\; P_{j}}}} \right)}.}} & (22)\end{matrix}$

The constraints (18) and (20) come from the definition of π. Constraint(19) follows from the average power constraint, and (21) is aconsequence of the symmetry assumption.

This problem is an extension to the two-carrier problem consideredabove. Actually, to vary power in time has no essential difference tovary power in the frequency domain, except that since time goes onforever, a finer allocation (or time-sharing) between different schemescan be obtained. If the system can have infinite number of carriers, theproblem to find the optimal power allocation across carriers issubstantially similar to the problem to find the optimal powerallocation in time.

Theorem 4: The maximum rate for a single user under the opportunisticpower allocation is determined by the solution to the followingoptimization problem

$\begin{matrix}{{\max\;\theta_{1}{\log_{2}\left( {1 + \frac{{hP}_{1}}{1 + {\eta\; h\; P_{1}}}} \right)}} + {\theta_{2}\frac{\log_{2}\left( {1 + {2\; h\; P_{2}}} \right)}{2}}} & (23) \\{{{{s.t.\mspace{50mu}\theta_{1}} + \theta_{2}} = 1};} & (24) \\{\mspace{79mu}{{{{\theta_{1}P_{1}} + {\theta_{2}P_{2}}} = P_{m}};}} & (25) \\{\mspace{79mu}{{0 \leq \theta_{1}},{\theta_{2} \leq 1.}}} & (26)\end{matrix}$

Remarks: As compared to the original infinite-dimensional optimizationproblem (17), the optimization problem here can be simpler. In (23), theoptimization has four parameters θ₁, θ₂, P₁ and P₂, and can beinterpreted as follows. The optimization (23) is essentially atime/power sharing between reuse-1 and reuse-2 scheme. θ₁ and θ₂correspond to the time fraction that the system is choosing reuse-1 andreuse-2 schemes, respectively. P₁ and P₂ are the power levels the systemchooses for reuse-1 and reuse-2, given the average power constraint canbe satisfied. In other words, this theorem reveals that among allpossible power allocation strategies, for any single mobile in thesystem, the optimal strategy to optimize its capacity within the systemcan be in the form of time/power sharing between reuse-1 and reuse-2.

It should be noted here the time/power sharing here is different fromthe time/power sharing scheme mentioned in the single cell case sincethere the sharing is between users while here the resource is sharedamong different transmitting strategies for the same user.

Proof: To prove this theorem, (17) can be optimized over all possibleprobability matrix π given a fixed set of power alphabet. After fixingP, it can be seen that C_(ij)'s are constant with respect to π and theproblem (17) becomes a linear programming problem.

Next the constraint (21) can be removed by reducing the number ofparameters to optimize.

$\begin{matrix}{\max_{\{{\pi_{ij}:{i \geq j}}\}}{\sum\limits_{i \geq j}^{\;}{\pi_{ij}\left( {C_{ij} + {C_{ji}I_{i \neq j}}} \right)}}} & (27) \\{{{s.t.\mspace{59mu}{\sum\limits_{\;{i \geq j}}^{\;}{\pi_{ij}\left( {1 + I_{i \neq j}} \right)}}} = 1};} & (28) \\{{{\underset{\mspace{124mu}{i \geq j}}{\overset{\;}{\sum}}\pi_{ij}P_{i}} = P_{m}};} & (29) \\{{{0 \leq \pi_{ij} \leq 1},{\forall i},j,}} & (30)\end{matrix}$where I_(i≠j) is the indicator function that i is not equal to j.

Another observation that can be made is that (28) already ensures thatπ_(ij)≦1, given that π_(ij)≧0, for all i,j. Thus, the linear constraintscan be now reduced to

$\begin{matrix}{{{\sum\limits_{\;{i \geq j}}^{\;}{\pi_{ij}\left( {1 + I_{i \neq j}} \right)}} = 1};} & (31) \\{{{\sum\limits_{\;{i \geq j}}^{\;}{\pi_{ij}P_{i}}} = P_{m}};} & (32)\end{matrix}$π_(ij)≧0,∀i,j.  (33)

Since the linear programming problem is optimized at one of the vertexesof the linear region, the vertexes of the region determined by (31)-(33)can be reviewed. For instance, optimizing {π_(ij): i≧j} can have at mosttwo non-zero entries.

It can be shown that the above is true if there are three π_(ij)'s (i≧j)to optimize over. In the three-dimensional space, the two constraints(31) and (32) restrict the feasible π_(ij)'s to be on a straight line.Thus, the vertexes of the convex region are nothing but the endpoints ofthe straight line when it hits one of the three plains: π_(ij)=0. (Ithas to hit the plains since the whole region is a bounded region.) Thus,one of the three parameters have to be zero, which proves the above forthe case of three π_(ij)'s. For the general case, this argument can beapplied to any non-zero three π_(ij)'s and shown that it does not reducethe optimality by considering only two out of three π_(ij)'s to benon-zero.

Therefore, for any power alphabet of any size, it does not lose anyoptimality by only assigning the probability to up to four power levels.Further, in the upper half (including the diagonal entries), it issufficient to consider only two non-zero π_(ij) entries. With thissimplification, three cases can be evaluated: (i) both non-zero entriesare not diagonal entries; (ii) one of the entries is a diagonal entry;and (iii) both entries are diagonal entries. However, in the case of(ii) and (iii), it can be considered as a special case of (i) byallowing the power alphabet to have identical entries. In view of this,the power alphabet can be assumed to be (P₁, P₂, P₃, P₄), and thenon-zero probability entries are π₁₂, π₂₁ and π₃₄, π₄₃.

Lemma 2 can be applied here and further it can be determined that P₁=P₂or one of P₁, P₂=0. In particular, the choice of P₁ and P₂ can beoptimized, without changing the average of them, which can yield thesame problem as the two-carrier two-cell single-user problem seen above,and thus, Lemma 2 is applicable here. Same argument holds for P₃ and P₄.In other words, both (P₁, P₂) and (P₃, P₄) are either reuse-1 orreuse-2. On the other hand, if both of them belong to the same reusescheme, either reuse-1 or reuse-2, there may be no motivation to choosedifferent power levels. This can be for reuse-2; for reuse-1, on theother hand, the concavity of the following function can be argued: log₂

$\left( {1 + \frac{x}{1 + {ax}}} \right),$which can be straightforward when evaluating the second-order derivativewith respect to x.

A numerical solution to the optimization problem in (23) can also beprovided. The solution is summarized in the following corollary.

Corollary 2: The capacity of a single user under opportunistic powerallocation with average power P_(m), or equivalently, the solution tothe optimization problem (17), is determined by the following equation:

$\begin{matrix}{{C\left( P_{m} \right)} = \left\{ \begin{matrix}\; & \; \\{\log_{2}\left( {1 + \frac{{hP}_{m}}{1 + {\eta\; h\; P_{m}}}} \right)} & {{{{if}\mspace{14mu} P_{m}} < P_{T\; 1}};} \\{{\frac{P_{m} - P_{T\; 1}}{P_{T\; 2} - P_{T\; 1}}{\log_{2}\left( {1 + \frac{{hP}_{T\; 1}}{1 + {\eta\; h\; P_{T\; 1}}}} \right)}} + {\frac{P_{T\; 2} - P_{m}}{P_{T\; 2} - P_{T\; 1}}\frac{1}{2}{\log_{2}\left( {1 + {2\;{hP}_{T\; 2}}} \right)}}} & {{{{if}\mspace{14mu} P_{T\; 1}} \leq P_{m} < P_{T\; 2}};} \\{\frac{1}{2}{\log_{2}\left( {1 + {2\; h\; P_{m}}} \right)}} & {{if\mspace{14mu} P_{m}} \geq {P_{T\; 2}.}}\end{matrix} \right.} & (34)\end{matrix}$where P_(T1) and P_(T2) are defined in FIG. 19.

FIG. 19 illustrates a solution to the single user power allocationproblem. As depicted, 1902 illustrates capacity under reuse 2, 1904shows capacity under reuse 1, 1906 illustrates a common tangential line,and 1908 represents a capacity. The line 1904 is the capacity withaverage power P_(m) under reuse 1, which is given by

${\log_{2}\left( {1 + \frac{{hP}_{m}}{1 + {\eta\; h\; P_{m}}}} \right)}.$The line 1902 is the capacity under reuse 2, which is given by ½log₂(1+2hP_(m)). The dashed line 1906 is a straight line which istangential to both capacity curves. P_(T1) and P_(T2) are the tangentialpoints of the common tangential line to the two capacity curves.

Again referring to FIG. 19, in the lower SNR regime, the reuse-1 curve1904 performs similar as compared to the reuse-2 capacity curve 1902since in the low SNR regime, the capacity scales linearly with thetransmit power regardless the how many degrees of freedom are used.However, as available power grows, reuse-1 starts to outperform reuse-2since the optimal strategy generally is to spread the available powerevenly across bandwidth. However, due to the existence of theinterferer, the reuse-1 capacity will be bounded by log₂

$\left( {1 + \frac{1}{\alpha}} \right)$as SNR grows while the reuse-2 SNR keeps growing logarithmatically.

This solution illustrates that when the available power P_(m) is lessthan P_(T1), which is determined given h and η for a mobile, thenreuse-1 is optimal. If the average power is larger than the otherthreshold P_(T2), then reuse-2 is optimal, where the transmittertransmits at 2 P_(m) half of the time and keeps silent in the other halfdegrees of freedom. When the average power P_(m) falls between the twothresholds, then a time/power sharing between reuse-1 and reuse-2 isoptimal. Further, when doing reuse-1, the transmitter should transmit atpower P_(T1); when doing reuse-2, the transmitter should transmit atpower 2P_(T2) when it is transmitting. This illustrates the optimaltransmitting strategy at a given power level.

An alternate angle to look at this problem is to find the optimaltransmitting strategy for different mobiles (with different h and η)given an average power constraint. For the mobiles which are close tothe transmitter, e.g., η<<1, the hard limit for the rate in reuse-1 caseis very large and the intersection point P_(T) can be out of the powerrange of interest. In this case, reuse-1 can be optimal for a powerconstraint. On the other hand, for cell boundary users, e.g., η iscomparable to, in this case, the reuse-1 curve can be compressed into asmall capacity region between 0 and probably a couple of bits persecond. In this case, the threshold power levels are moved to close to 0and for any reasonable power constraint, reuse-2 is optimal, amongpossible transmitting strategies.

A relation exists between Corollary 2 and Lemma 2. Lemma 2 focused onthe scenario where the system has two carriers and discussed the bestway to allocate power between the two carriers to maximize the rate fora single user in the primary cell. This is equivalent to find theoptimal opportunistic power allocation scheme if restricted to a poweralphabet size of 2 and a probability matrix with zero diagonal entries.It shows that there is a single threshold for the average power

$P_{T} = \frac{1 - {2\alpha}}{2\; h\;\alpha^{2}}$such that if P_(m)>P_(t), reuse-2 is optimal and otherwise reuse-1 isoptimal. It can be seen that P_(T) corresponds to the intersection pointof reuse-1 and reuse-2 capacity curves in FIG. 19. Thus, removing theconstraints on the alphabet size and the probability matrix above helpsimprove the capacity for P_(m)ε(P_(T1), P_(T2)).

Proof: Achievability is trivial if the above transmitting strategy isemployed. For the converse, Theorem 4 has narrowed down the optimaltransmitting strategy to a much smaller set of strategies as describedin (23). Thus, it can be shown that by doing time/power sharing betweenreuse-1 and reuse-2, better results than curve 1908 may not be obtained.This is again true since any achievable rate tuple under time/powersharing between reuse-1 and reuse-2 lies on one of the straight linesconnecting two points: one on the reuse-1 curve and the other on thereuse-2 curve.

Capacity region under opportunistic power allocation: The capacityregion for two users in the primary cell under opportunistic powerallocation can be analyzed. An achievability region can be shown whichimproves upon the capacity region depicted in FIG. 18. This regionroughly estimates the improvement that can be yielded as compared to thecapacity region under simple reuse-1 schemes.

A strategy is to do time-sharing between reuse-1 and reuse-2. This willachieve a capacity region for rate tuples under a straight lineconnecting the two extreme points under reuse-1 and reuse-2 in FIG. 18.This linear region can be further improved by using the same strategy asused for the single user scenario, e.g., do time/power sharing betweenreuse 1 and reuse 2. By doing this, the achievable rate region can becharacterized as the following lemma.

Lemma 3: For a single-carrier two-cell system, assume that the two usersin the primary cell are characterized by (h₁, η₁) (h₂, η₂) and satisfythat h₂≧h₁ and η₂≦η₁, e.g., user 1 is a good user and user 2 is a baduser. The capacity region for these two users is lower bounded by thefollowing rate region

$\left\{ {{{\left( {{\theta\;\frac{\log_{2}\left( {1 + {2\; h_{1}P_{1}}} \right)}{2}},{\left( {1 - \theta} \right){\log_{2}\left( {1 + \frac{h_{2}P_{2}}{1 + {\alpha_{2}h_{2}P_{2}}}} \right)}}} \right)\text{:}0} \leq \theta \leq 1},{{{\theta\; P_{1}} + {\left( {1 - \theta} \right)P_{2}}} = P_{m}}} \right\}.$

The achievable rate region can be compared to the simple reuse-1 andreuse-2 scheme. As shown in FIG. 20, the region is a superset to eitherthe reuse-1 or reuse-2 scheme. FIG. 20 illustrates an achievable rateregion under opportunistic power allocation. Moreover, line 2002represents a reuse-1 capacity region, line 2004 depicts a reuse-2capacity region, line 2006 illustrates time sharing between reuse-1 andreuse-2, line 2008 depicts time/power sharing between reuse-1 andreuse-2, and line 2010 illustrates time/power sharing between reuse-1and (P₁, P₂). The achievable rate region can be superior to the regionbased on time-sharing between reuse-1 and reuse-2 too by giving anotherfreedom to share power as well. Thus, by doing this scheme, capacitygain can be achieved against the traditional reuse-1 scheme.

By using a time/power sharing between reuse-1 and reuse-2, a restrictionto a power alphabet of size 3, with one the alphabet being 0, can beutilized. However, it is not clear a priori that such choices areoptimal or close to optimal in the case of multiple users although itcan be known that they are optimal in the single-user scenario. Next itcan be shown that for the two user case, to consider a power levelalphabet of size 4 is sufficient.

Theorem 5: Every rate tuple within the capacity region for the two usersin a two-cell system under opportunistic power allocation can beachieved by a power allocation scheme with a power level alphabet ofsize 4.

Proof: Apparently, it suffices to show that the statement is true forall rate tuple on the boundary of the capacity region. First, thecapacity region can be a convex region under opportunistic powerallocation. This is true since any two rate tuples within the capacityregion, a simple time-sharing strategy can achieve all rate tuples onthe straight line connecting these two tuples. In other words, they arewithin the capacity region as well, which shows the convexity of theregion.

An important property for a convex region is that for any point lying onthe boundary of the region, a tangential straight line can be found suchthat the whole region is on one side of the straight line. Thus, for anypoint (R₁, R₂) on the boundary, a set of linear parameters w₁ and w₂ canbe found such that (R₁, R₂) is the solution to the followingoptimization problem:max w₁R₁+w₂R₂  (35)s.t.(R₁,R₂)εΛ,  (36)if Λ denotes the capacity region under opportunistic power allocation.Further, this problem can be written more explicitly as follows:

$\begin{matrix}{\max_{P,\pi,\beta}{\sum\limits_{ij}^{\;}{\pi_{ij}\left( {{w_{1}\beta_{ij}{\log_{2}\left( {1 + \frac{h_{1}P_{i}}{1 + {\eta_{1}h_{1}P_{j}}}} \right)}} + {{w_{2}\left( {1 - \beta} \right)}{\log_{2}\left( {1 + \frac{h_{2}P_{i}}{1 + {\eta_{2}h_{2}P_{j}}}} \right)}}} \right)}}} & (37) \\{\mspace{95mu}{{{s.t.\mspace{40mu}{\sum\limits_{ij}^{\;}\pi_{ij}}} = 1};}} & (38) \\{\mspace{166mu}{{{\sum\limits_{ij}^{\;}{\pi_{ij}P_{i}}} = P_{m}};}} & (39)\end{matrix}$0≦π_(ij)≦1,∀i,j;  (40)π_(ij)=π_(ji);  (41)0≦β_(ij)≦1,∀i,j.  (42)

The optimization over {β_(ij)} given the power allocation alphabet P andthe joint probability matrix {π_(ij)} is trivial. From (37), it can beapparent to assign the user with better weighted capacity in stateπ_(ij). Thus, the objective function (37) can be simplified to

$\max\limits_{P,\pi}{\sum\limits_{ij}^{\;}{{\pi_{ij}\left( {\max\left( {{w_{1}{\log_{2}\left( {1 + \frac{h_{1}P_{i}}{1 + {\eta_{1}h_{1}P_{j}}}} \right)}},{w_{2}{\log_{2}\left( {1 + \frac{h_{2}P_{i}}{1 + {\eta_{2}h_{2}P_{j}}}} \right)}}} \right)} \right)}.}}$

Optimization over π given any set of alphabet P can be considered. Thisis again a linear programming problem and the argument used in the proofof Theorem 4 can be employed. A conclusion can be reached thatoptimality is not lost by focusing on alphabets with size 4 and thecorresponding joint probability matrix with at most four non-zeroentries: π₁₂, π₂₁, π₃₄, π₄₃. By trying all possible choices of P, π andall possible scheduling policies under this constraint, the wholecapacity region can be achieved.

Remarks: Although Theorem 5 does not provide a closed-form expressionfor the capacity region, it significantly reduces the complexity of theoriginal optimization problem (37) to an optimization problem with eightparameters. On the other hand, it also shows that the time/power sharingbetween reuse-1 and reuse-2 can not be too far away from the optimalcapacity region since in general, any point within the capacity regionshould be able to be achieved by time/power sharing with two generalreuse schemes: (P₁, P₂) and (P₃, P₄). A conjecture that can be made isthat one of the reuse schemes should be the reuse-1 scheme, e.g., P₃=P₄.Thus, a better scheme which might outperform time/power sharing betweenreuse-1 and reuse-2 is to do time/power sharing between reuse-1 and (P₁,P₂). An advantage of this scheme can be significant especially when P₂is chosen to be a small power instead of zero. Of course, according tothe scheduling guideline observed herein, the good user can be scheduledin this close-to-zero carrier. By doing this, the available degrees forthe good users can be increased by taking a small hit on the SNR of thebad users scheduled in P₁. Overall, better points can be achieved ascompared to the capacity region under time/power sharing between reuse-1and reuse-2. This observation is also shown in FIG. 20.

All the curves shown in FIG. 20 can be achievable curves under certainpower reuse schemes in the time domain or the frequency domain. Thebenefit of doing this now can be significant. For all or nearly allpractical systems, the operating point won't sit on the end point of (0,R₂). For any other operating point, an improvement can be provided byusing smarter power reuse schemes than the simple reuse-1 scheme. Themore cell-edge users in the system, the more benefit obtained.

Moreover, this improvement won't go away even when the one-user-per-slotconstraint is removed. In other words, in multi-cell scenario, a gooddesign within the carrier is not sufficient to take good care of theinter-cell interference. Collaboration in different carriers/time slotsand joint power allocation and scheduling can improve the performance ofall types of users in the system.

Breathing cells: opportunistic power allocation in the multi-cellscenario. The above theoretic analysis can indicate that varying poweracross time and/or frequency is beneficial for the overall systemperformance, without introducing too much complexity to the system.Further, scheduling can be done in such a way that good users are mostlyscheduled in the bad carriers/time-slots, while the bad users are mostlyscheduled in the good carriers/time-slots. In the single cell scenario,the gain by doing this is not so significant. On the other hand, thepotential gain by doing this scheme when inter-cell interference existscan be very important since now for the cell boundary users, the powergain can now easily compensate for the loss in segments. This benefitcan be seen in the capacity region comparison as shown above.

In a typical multi-cell cellular deployment, around thirty percent ofthe users can have an average SNR below 0 dB due to the inter-cellinterference. This plays a key bottleneck to the system performance forboth data and delay-sensitive applications. Thus, one would expect thatsimilar schemes can be utilized to smartly reuse power across carriersor time to improve the system spectral efficiency. Accordingly, a schemecan be leveraged to extend the intuitions achieved in the single-celland two-cell cases to the multi-cell scenarios, and qualitativelyanalyze the potential gain that can be achieved by introducing theseschemes in the current cellular networks.

Power allocation patterns and their reuse over the network: The schemeproposed here is called the breathing-cell scheme, where each cellvaries its transmit power limit in a slow pace (as compared to thecommunication time scale), and in a cooperative way, e.g., a celltransmits at high power when the others are transmitting at relativelylow power. An example is shown in FIG. 12. In this example, each cellvaries its power between −P_(m) and P_(m) with a period of 100 timeslots. For adjacent cells, they choose different power level types tocreate fluctuations in SNRs, as shown in FIG. 10.

A slow-time-scale power variation can be chosen since in a practicalsystem, it may not desirable to have the power varying too rapidlybecause of the following considerations: (1) the mobile can havedifficulty to track the channel variation if the power varies too fast;and (2) it is not desirable to require too much synchronization betweendifferent base stations.

Scheduling in breathing cells: With this opportunistic power allocationscheme, stationary users in the system can see channel fluctuations.However, the channel fluctuations are highly correlated across users.For example, when the cell's allocated power curve goes up, and theneighboring cells' power goes down, all users within the cell will seechannel quality improvement. Similar to the above observations, in suchscenarios, a good way is to schedule a good user when the channel is badand to schedule a bad user when the channel is good. In the two usercase, this guideline is simple enough to implement. However, in the moreinteresting multi-user scenario, it is not that straight forward to finda simple scheduling rule to choose user wisely and fairly.

The proportional-fair scheduler can solve this problem. In theproportional-fair scheduler, the scheduler picks user k* in each timeslot with the largest R_(k)(t)/T_(k)(t), where R_(k)(t) is the estimatedrate that user k can transmit if scheduled based on its SNR report andT_(k)(t) is the average throughput of user k in history. Inimplementations, T_(k)(t) can be calculated over a comparatively longsliding window as compared to the communication scale, since the channelof a moving user can be non-ergotic. The window size also reflects themaximum tolerable delay in scheduling. This scheduler can be shown tomaximize the system utility of Σ_(k) log(T_(k)), where T_(k) is thelong-term average throughput of user k.

In the case of symmetric user channel conditions, e.g., the distributionof the channel conditions between users can be substantially similar,and the proportional fair scheduler can pick the user with the bestchannel condition. Thus, all users will be picked when their channelconditions are relatively good as compared to the average levels and themore users in the system, the better chance that a user will be pickedat its best possible channel. From a system point of view, it looks likethe system's sum throughput is increasing as the number of users areincreasing and this phenomena is referred to as the multi-userdiversity. With multi-user diversity, tractable channelfading/variations can actually bring benefit to the system.

However, in breathing cells, the proportional fair scheduler behavesdifferently. First of all, the channel quality of users is highlycorrelated assuming users are stationary and the channel quality isfully determined by the power allocation variation across time. FIG. 21and FIG. 22 show the channel condition and normalized schedulable ratefor different users in the breathing-cell scheme.

In particular, FIG. 21 illustrates channel conditions for two userswithin the same cell under breathing cells where both channel gains canbe normalized by the average channel gain of the good user. Further,FIG. 22 illustrates variations of R_(k)/T_(k) for different users. FIG.22 can provide information about how a proportional fair scheduler picksusers in a particular case. Again, due to the concavity of capacity,when the channel condition improves for both users, the effect for thebad user is more important in terms of R_(k)/T_(k); when the channelcondition deteriorates, the good user takes a lower decrease inR_(k)/T_(k). As a consequence, the scheduler picks the good user whenthe channel is bad and picks the bad user when the channel is good.

Another salient feature of the breathing-cell design is that theinter-cell interferences experienced by different users are notsynchronized in a multi-cell scenario. This can be because the maininterfering cells to users at different locations are breathing withdifferent patterns. This adds another degree of variations to the curveof R_(k)/T_(k) as shown in FIG. 22. Thus, in different time slots, thescheduler can favor the users experiencing less inter-cell interference.

Delay-sensitive applications: An issue of the breathing-cell design canbe related to performance associated with delay-sensitive traffic. Insuch case, the system does not have so much freedom to schedule thetraffic in terms of waiting for the right moment. By artificiallyintroducing channel fluctuations to all the users, long outage periodscan be introduced for cell boundary users. Accordingly, extensions ofthis design can address this issue.

In a multi-carrier system, a possible remedy is to reuse the powervariation pattern across carriers too. For example, suppose there arethree carriers per cell. A power allocation pattern can be assigned andas a consequence, at each time slot, there can be at least one carrierhaving better SNR as compared to the simple Reuse-1 scheme. Thescheduler gives priority to the delay-sensitive traffic over the elastictraffic and first schedules them to be transmitted over the channel. Itcan be noted that it may not always be beneficial to schedule the delaysensitive traffic on the best carrier at the moment since it might causeleft-overs for the best carrier and reduce the possible benefit for theelastic traffic. A guideline can be to schedule the delay sensitivetraffic on the worst carrier(s) which are capable of depleting thedelay-sensitive queue.

Such an extension can be utilized when all mobiles, includingdelay-sensitive mobiles, are wideband mobiles. This assumption might notbe true for VOIP type of mobile. For a multi-carrier system with a lotof narrow-band delay-sensitive mobiles, another system design can be todo the fixed power reuse approach instead of the breathing-cell scheme.If the number of carriers within each cell is large, there may be nodifference between vary the power across time or across carriers. Thesame power level variation levels can be assigned as thepower-allocation schemes over multiple carriers. In the case of threecarriers per sector, this leads to Flexband design. In this case, thescheduler problem for delay-sensitive users is partly shifted to theadmission controller. A similar rule to the scheduling guidelinementioned above can be applied here such that a delay-sensitive mobileis admitted to the worst qualified carrier, which is capable of deliverthe traffic from the mobile without causing outage. On the other hand,the other wideband data mobiles can still take advantage of a similarbenefit as seen in breathing cells.

The single-carrier network with delay-sensitive users can be considered.In this case, apparently, none of the schemes seen above may help ifslow variation over transmit power is adopted in all the cells. In thiscase, actually, a TDD-type of design can at least mitigate the problemthat the breathing-cell design causes for delay-sensitive users. The TDDhere is not between uplink and downlink, but between different transmitmodes determined by transmit power. For example, one can choose threedifferent power levels and each cell chooses a specific order ofiterating these three power levels. For elastic users, the benefit ofdoing this is similar to the Flexband design with three carriers eachcell. For delay sensitive users, the outage period is much shorter nowas compared to the breathing-cell design. However, this scheme leveragesglobal synchronization, which is available in TDD networks, but not inFDD networks. Also, this introduces more complexity to the system. Forexample, the scheduler has to track three different SNR levels for allmobiles to make the scheduling decision.

Comparison to opportunistic beamforming: There is similarity betweenthis scheme and the opportunistic beamforming scheme utilized for amultiple antenna downlink. In opportunistic beamforming, the basestation uses multiple antennas to form one or multiple beams and sweepsacross the users within the cell. This is done by varying the power andphase for the signals fed into different antennas in a slow time scale.

Comparing the two schemes, there are a lot of similarities. First, bothschemes try to introduce trackable channel fluctuations to stationarychannels so that the system can benefit from multiuser diversity.Second, they both have problems in dealing with delay-sensitive traffic.However, the approaches proposed above also can be used foropportunistic beam-forming with slight modifications. Finally, the gainfrom opportunistic beam-forming will disappear if all channels areRayleigh-faded. The breathing-cell design also suffers fromRayleigh-faded channel since in that case, the multi-user diversityboosts the SNR of all users at the times of being scheduled. The gain ofthe breathing-cell design mainly comes from the fact that the power gaincan be translated to a better capacity gain for poor users in thereuse-1 scheme. However, the multi-user diversity caused by fadingchannels makes everyone a better user and thus reduces the potentialgain we can achieve through breathing cells.

However, there are also some differences between the two schemes:

(1) Multiple antennas are not required to achieve the capacity gain inbreathing cells. Thus the system complexity is much less as compared tothe system with opportunistic beamforming.

(2) The gain of breathing cells is more significant when multiple cellsexists. The opportunistic beamforming can see most of its gain even witha single cell.

(3) The gain of breathing cells can only be seen when each cell hasmobiles with different SNRs. This is a valid assumption in a loadedsystem. However, when all the mobiles are close-to-base station mobiles,breathing cells can actually lead to a capacity loss. On the other hand,the opportunistic beamforming can still see a substantial gain when theSNRs of all mobiles are similar. The constraint there, though, is thatthe mobiles have to differ in angular directions. As a summary, thebreathing-cell approach differentiates users according to their distanceto the base station, while the opportunistic beamforming mainlydifferentiates mobiles with different em angular direction.

(4) The scheduler behaves differently in breathing cells. Here, it isnot possible to schedule all the users at their peaks. On the contrary,for the good users, the scheduler prefers to schedule them in badchannel conditions. Of course, they can be scheduled much more often inbreathing cells as compared to the reuse-1 case since a lot of resourcesare saved by scheduling.

Referring to FIGS. 23-25, methodologies relating to power allocation ina wireless communication network are illustrated. While, for purposes ofsimplicity of explanation, the methodologies are shown and described asa series of acts, it is to be understood and appreciated that themethodologies are not limited by the order of acts, as some acts may, inaccordance with one or more embodiments, occur in different ordersand/or concurrently with other acts from that shown and describedherein. For example, those skilled in the art will understand andappreciate that a methodology could alternatively be represented as aseries of interrelated states or events, such as in a state diagram.Moreover, not all illustrated acts may be required to implement amethodology in accordance with one or more embodiments.

Turning to FIG. 23, illustrated is a methodology 2300 that facilitatesoperating a communication network including a wireless communicationbase station that includes a first sector. At 2302, a first channel canbe transmitted on at a first power level from the first sector during afirst time period based on a first predetermined pattern (e.g., powerallocation pattern). Further, the first channel can include a firstfrequency bandwidth (e.g., carrier). At 2304, the first channel can betransmitted on at a second power level from the first sector during asecond time period based on the first predetermined pattern. Moreover,the second power level can be at least 0.5 dB different from the firstpower level.

The transmissions can occur upon a single carrier; however, it iscontemplated that multiple carriers can be utilized. Moreover, accordingto another example, channel quality report(s) can be received from oneor more mobile devices and based upon these reports the first channelcan be scheduled; thus, the first channel can be transmitted upon to theone or more mobile devices. Pursuant to an illustration, the firstsector and a second sector can be included in a common cell; thus, asector-wise reuse scheme can be leveraged. According to anotherembodiment (e.g., cell-wise reuse), the first sector can be included ina first cell, where disparate sector(s) of the first cell enabletransmitting at substantially similar power levels as the first sectorduring each time period, and a second sector can be included in a secondcell, where differing sector(s) of the second cell allow transmitting atsubstantially similar power levels as the second sector during each timeperiod.

It is contemplated that the transmissions can be assigned according to ascheme that can coordinate sectors and/or cells to enhance spectralefficiency. For example, the scheme can leverage discrete power levelsthat can be allotted in a time division manner. According to anotherillustration, respective smooth power allocation pattern curves can beallocated to the first sector and the second sector; these smooth powerallocation pattern curves can set forth the power level for the sectoras a function of time.

By way of further illustration, the first wireless communication basestation can include a second sector. As such, a second channel can betransmitted on at a third power level from the second sector during thefirst time period based on a second predetermined pattern. Further, thesecond channel can include a second frequency bandwidth, where the firstfrequency bandwidth and the second frequency bandwidth can have at least50% frequency bandwidth in common (e.g., a single carrier can beemployed). Moreover, the second channel can be transmitted on at afourth power level from the second sector during the second time periodbased on the second predetermined pattern. The fourth power level, forinstance, can be at least 0.5 dB different from the third power level.Additionally, the first power level can be within 0.5 dB of the thirdpower level and the second power level can be within 0.5 dB of thefourth power level. According to another example, it is to beappreciated that the first predetermined pattern and the secondpredetermined pattern can be substantially similar.

Pursuant to another example, the communication network can include asecond wireless communication base station that can include the secondsector described above. Accordingly, the first power level can be atleast 0.5 dB greater than the third power level, while the second powerlevel can be at least 0.5 dB less than the fourth power level. Moreover,the first predetermined pattern and the second predetermined pattern canboth be periodical. It is to be appreciated that these predeterminedpatterns can have dissimilar periods and/or substantially similarperiods. Further, the first and second predetermined patterns can havesubstantially similar periods with differing phases.

Turning to FIG. 24, illustrated is a methodology 2400 that facilitatesadaptively assigning power allocation patterns for allocating powerlevels. At 2402, an adaptive power allocation pattern can be selectedbased upon load information. For instance, load information can beshared amongst sector(s) and/or cell(s). Further, the load informationcan be leveraged to compare respective loads corresponding to eachsector and/or cell. Power allocation patterns can be shifted toaccommodate the analyzed loads; for example, a mean power level can beshifted up or down based upon a respective load. At 2404, power levelscan be assigned as a function of time based upon the power allocationpattern. The power allocation pattern, for example, can be a sinusoidalcurve that provides a power level as a function of time. At 2406,transmission can occur according to the assigned power levels.

Now referring to FIG. 25, illustrated is a methodology 2500 thatfacilitates operating a multiple carrier communication network includinga first wireless communication base station that includes a firstsector. At 2502, a first channel can be transmitted on at a first powerlevel from the first sector during a first time period based on a firstpredetermined pattern. For instance, the first channel can include afirst frequency bandwidth. At 2504, the first channel can be transmittedon at a second power level from the first sector during a second timeperiod based on the first predetermined pattern. At 2506, a secondchannel can be transmitted on at a third power level from the firstsector during the first time period based on a second predeterminedpattern. Further, the second channel can include a second frequencybandwidth. Moreover, the first frequency bandwidth and the secondfrequency bandwidth can be non-overlapping. At 2508, the second channelcan be transmitted on at a fourth power level from the first sectorduring the second time period based on the second predetermined pattern.The second power level can be at least 0.5 dB different from the firstpower level and the fourth power level can be at least 0.5 dB differentfrom the second power level. Additionally, a sum of the first powerlevel and the third power level can be within 0.5 dB of a sum of thesecond power level and the fourth power level. Further, the firstpredetermined pattern and the second predetermined pattern can beperiodical with substantially similar periods and disparate phases.Moreover, channel quality reports can be received from one or moremobile devices and transmission of the first channel and/or the secondchannel to the mobile device(s) can be scheduled as a function of thechannel quality reports.

According to another example, a second sector can also providetransmissions. The second sector can be included with the first sectorin the first wireless communication base station. Alternatively, thesecond sector can be included in a second wireless communication basestation. Moreover, a third channel can be transmitted on at a fifthpower level from the second sector during the first time period based ona third predetermined pattern. The third channel can include a thirdfrequency bandwidth that can have at least 50% frequency bandwidth incommon with the first frequency bandwidth. Also, the third channel canbe transmitted on at a sixth power level from the second sector duringthe second time period based on the third predetermined pattern.Additionally, a fourth channel can be transmitted on at a seventh powerlevel from the second sector during the first time period based on afourth predetermined pattern, where the fourth channel can include afourth frequency bandwidth that does not overlap with the thirdfrequency bandwidth in frequency. Further, the fourth frequencybandwidth can have at least 50% frequency bandwidth in common with thesecond frequency bandwidth. Moreover, the fourth channel can betransmitted on at an eighth power level from the second sector duringthe second time period based on the fourth predetermined pattern.

These transmissions can be effectuated within a common sector. Moreover,it is contemplated that any number of sub-carriers can be supported bythe common sector; the claimed subject matter is not limited toutilization of two sub-carriers. Further, it is to be appreciated thatsector-wise or cell-wise reuse can be utilized in the wirelesscommunication network. Additionally, the power levels can be allocatedbased upon a predetermined and/or adaptive scheme as described herein.

It will be appreciated that, in accordance with one or more aspectsdescribed herein, inferences can be made regarding allocating powerlevels in a wireless communication network. As used herein, the term to“infer” or “inference” refers generally to the process of reasoningabout or inferring states of the system, environment, and/or user from aset of observations as captured via events and/or data. Inference can beemployed to identify a specific context or action, or can generate aprobability distribution over states, for example. The inference can beprobabilistic—that is, the computation of a probability distributionover states of interest based on a consideration of data and events.Inference can also refer to techniques employed for composinghigher-level events from a set of events and/or data. Such inferenceresults in the construction of new events or actions from a set ofobserved events and/or stored event data, whether or not the events arecorrelated in close temporal proximity, and whether the events and datacome from one or several event and data sources.

According to an example, one or more methods presented above can includemaking inferences pertaining to determining respectively loadsencountered by neighboring sector(s) and/or cell(s). In accordance withanother example, loading information can be leveraged to infer how toadapt power allocation patterns accordingly. It will be appreciated thatthe foregoing examples are illustrative in nature and are not intendedto limit the number of inferences that can be made or the manner inwhich such inferences are made in conjunction with the variousembodiments and/or methods described herein.

FIG. 26 depicts an example communication system 2600 implemented inaccordance with various aspects including multiple cells: cell I 2602,cell M 2604. Note that neighboring cells 2602, 2604 overlap slightly, asindicated by cell boundary region 2668. Each cell 2602, 2604 of system2600 includes three sectors. Cells which have not been subdivided intomultiple sectors (N=1), cells with two sectors (N=2) and cells with morethan 3 sectors (N>3) are also possible in accordance with variousaspects. Cell 2602 includes a first sector, sector I 2610, a secondsector, sector II 2612, and a third sector, sector III 2614. Each sector2610, 2612, 2614 has two sector boundary regions; each boundary regionis shared between two adjacent sectors.

Cell I 2602 includes a base station (BS), base station I 2606, and aplurality of end nodes (ENs) (e.g., wireless terminals) in each sector2610, 2612, 2614. Sector I 2610 includes EN(1) 2636 and EN(X) 2638;sector II 2612 includes EN(1′) 2644 and EN(X′) 2646; sector III 2614includes EN(1″) 2652 and EN(X″) 2654. Similarly, cell M 2604 includesbase station M 2608, and a plurality of end nodes (ENs) in each sector2622, 2624, 2626. Sector I 2622 includes EN(1) 2636′ and EN(X) 2638′;sector II 2624 includes EN(1′) 2644′ and EN(X′) 2646′; sector 3 2626includes EN(1″) 2652′ and EN(X″) 2654′.

System 2600 also includes a network node 2660 which is coupled to BS I2606 and BS M 2608 via network links 2662, 2664, respectively. Networknode 2660 is also coupled to other network nodes, e.g., other basestations, AAA server nodes, intermediate nodes, routers, etc. and theInternet via network link 2666. Network links 2662, 2664, 2666 may be,e.g., fiber optic cables. Each end node, e.g., EN(1) 2636 may be awireless terminal including a transmitter as well as a receiver. Thewireless terminals, e.g., EN(1) 2636 may move through system 2600 andmay communicate via wireless links with the base station in the cell inwhich the EN is currently located. The wireless terminals, (WTs), e.g.,EN(1) 2636, may communicate with peer nodes, e.g., other WTs in system2600 or outside system 2600 via a base station, e.g., BS 2606, and/ornetwork node 2660. WTs, e.g., EN(1) 2636 may be mobile communicationsdevices such as cell phones, personal data assistants with wirelessmodems, etc.

FIG. 27 illustrates an example base station 2700 in accordance withvarious aspects. Base station 2700 implements tone subset allocationsequences, with different tone subset allocation sequences generated forrespective different sector types of the cell. Base station 2700 may beused as any one of base stations 2606, 2608 of the system 2600 of FIG.26. The base station 2700 includes a receiver 2702, a transmitter 2704,a processor 2706, e.g., CPU, an input/output interface 2708 and memory2710 coupled together by a bus 2709 over which various elements 2702,2704, 2706, 2708, and 2710 may interchange data and information.

Sectorized antenna 2703 coupled to receiver 2702 is used for receivingdata and other signals, e.g., channel reports, from wireless terminalstransmissions from each sector within the base station's cell.Sectorized antenna 2705 coupled to transmitter 2704 is used fortransmitting data and other signals, e.g., control signals, pilotsignal, beacon signals, etc. to wireless terminals 2800 (see FIG. 28)within each sector of the base station's cell. In various aspects, basestation 2700 may employ multiple receivers 2702 and multipletransmitters 2704, e.g., an individual receiver 2702 for each sector andan individual transmitter 2704 for each sector. Processor 2706, may be,e.g., a general purpose central processing unit (CPU). Processor 2706controls operation of base station 2700 under direction of one or moreroutines 2718 stored in memory 2710 and implements the methods. I/Ointerface 2708 provides a connection to other network nodes, couplingthe BS 2700 to other base stations, access routers, AAA server nodes,etc., other networks, and the Internet. Memory 2710 includes routines2718 and data/information 2720.

Data/information 2720 includes data 2736, tone subset allocationsequence information 2738 including downlink strip-symbol timeinformation 2740 and downlink tone information 2742, and wirelessterminal (WT) data/info 2744 including a plurality of sets of WTinformation: WT 1 info 2746 and WT N info 2760. Each set of WT info,e.g., WT 1 info 2746 includes data 2748, terminal ID 2750, sector ID2752, uplink channel information 2754, downlink channel information2756, and mode information 2758.

Routines 2718 include communications routines 2722 and base stationcontrol routines 2724. Base station control routines 2724 includes ascheduler module 2726 and signaling routines 2728 including a tonesubset allocation routine 2730 for strip-symbol periods, other downlinktone allocation hopping routine 2732 for the rest of symbol periods,e.g., non strip-symbol periods, and a beacon routine 2734.

Data 2736 includes data to be transmitted that will be sent to encoder2714 of transmitter 2704 for encoding prior to transmission to WTs, andreceived data from WTs that has been processed through decoder 2712 ofreceiver 2702 following reception. Downlink strip-symbol timeinformation 2740 includes the frame synchronization structureinformation, such as the superslot, beaconslot, and ultraslot structureinformation and information specifying whether a given symbol period isa strip-symbol period, and if so, the index of the strip-symbol periodand whether the strip-symbol is a resetting point to truncate the tonesubset allocation sequence used by the base station. Downlink toneinformation 2742 includes information including a carrier frequencyassigned to the base station 2700, the number and frequency of tones,and the set of tone subsets to be allocated to the strip-symbol periods,and other cell and sector specific values such as slope, slope index andsector type.

Data 2748 may include data that WT1 2800 has received from a peer node,data that WT1 2800 desires to be transmitted to a peer node, anddownlink channel quality report feedback information. Terminal ID 2750is a base station 2700 assigned ID that identifies WT 1 2800. Sector ID2752 includes information identifying the sector in which WT1 2800 isoperating. Sector ID 2752 can be used, for example, to determine thesector type. Uplink channel information 2754 includes informationidentifying channel segments that have been allocated by scheduler 2726for WT1 2800 to use, e.g., uplink traffic channel segments for data,dedicated uplink control channels for requests, power control, timingcontrol, etc. Each uplink channel assigned to WT1 2800 includes one ormore logical tones, each logical tone following an uplink hoppingsequence. Downlink channel information 2756 includes informationidentifying channel segments that have been allocated by scheduler 2726to carry data and/or information to WT1 2800, e.g., downlink trafficchannel segments for user data. Each downlink channel assigned to WT12800 includes one or more logical tones, each following a downlinkhopping sequence. Mode information 2758 includes information identifyingthe state of operation of WT1 2800, e.g. sleep, hold, on.

Communications routines 2722 control the base station 2700 to performvarious communications operations and implement various communicationsprotocols. Base station control routines 2724 are used to control thebase station 2700 to perform basic base station functional tasks, e.g.,signal generation and reception, scheduling, and to implement the stepsof the method of some aspects including transmitting signals to wirelessterminals using the tone subset allocation sequences during thestrip-symbol periods.

Signaling routine 2728 controls the operation of receiver 2702 with itsdecoder 2712 and transmitter 2704 with its encoder 2714. The signalingroutine 2728 is responsible for controlling the generation oftransmitted data 2736 and control information. Tone subset allocationroutine 2730 constructs the tone subset to be used in a strip-symbolperiod using the method of the aspect and using data/information 2720including downlink strip-symbol time info 2740 and sector ID 2752. Thedownlink tone subset allocation sequences will be different for eachsector type in a cell and different for adjacent cells. The WTs 2800receive the signals in the strip-symbol periods in accordance with thedownlink tone subset allocation sequences; the base station 2700 usesthe same downlink tone subset allocation sequences in order to generatethe transmitted signals. Other downlink tone allocation hopping routine2732 constructs downlink tone hopping sequences, using informationincluding downlink tone information 2742, and downlink channelinformation 2756, for the symbol periods other than the strip-symbolperiods. The downlink data tone hopping sequences are synchronizedacross the sectors of a cell. Beacon routine 2734 controls thetransmission of a beacon signal, e.g., a signal of relatively high powersignal concentrated on one or a few tones, which may be used forsynchronization purposes, e.g., to synchronize the frame timingstructure of the downlink signal and therefore the tone subsetallocation sequence with respect to an ultra-slot boundary.

FIG. 28 illustrates an example wireless terminal (e.g., end node, mobiledevice, . . . ) 2800 which can be used as any one of the wirelessterminals (e.g., end nodes, mobile devices, . . . ), e.g., EN(1) 2636,of the system 2600 shown in FIG. 26. Wireless terminal 2800 implementsthe tone subset allocation sequences. Wireless terminal 2800 includes areceiver 2802 including a decoder 2812, a transmitter 2804 including anencoder 2814, a processor 2806, and memory 2808 which are coupledtogether by a bus 2810 over which the various elements 2802, 2804, 2806,2808 can interchange data and information. An antenna 2803 used forreceiving signals from a base station 2700 (and/or a disparate wirelessterminal) is coupled to receiver 2802. An antenna 2805 used fortransmitting signals, e.g., to base station 2700 (and/or a disparatewireless terminal) is coupled to transmitter 2804.

The processor 2806 (e.g., a CPU) controls operation of wireless terminal2800 and implements methods by executing routines 2820 and usingdata/information 2822 in memory 2808.

Data/information 2822 includes user data 2834, user information 2836,and tone subset allocation sequence information 2850. User data 2834 mayinclude data, intended for a peer node, which will be routed to encoder2814 for encoding prior to transmission by transmitter 2804 to basestation 2700, and data received from the base station 2700 which hasbeen processed by the decoder 2812 in receiver 2802. User information2836 includes uplink channel information 2838, downlink channelinformation 2840, terminal ID information 2842, base station IDinformation 2844, sector ID information 2846, and mode information 2848.Uplink channel information 2838 includes information identifying uplinkchannels segments that have been assigned by base station 2700 forwireless terminal 2800 to use when transmitting to the base station2700. Uplink channels may include uplink traffic channels, dedicateduplink control channels, e.g., request channels, power control channelsand timing control channels. Each uplink channel includes one or morelogic tones, each logical tone following an uplink tone hoppingsequence. The uplink hopping sequences are different between each sectortype of a cell and between adjacent cells. Downlink channel information2840 includes information identifying downlink channel segments thathave been assigned by base station 2700 to WT 2800 for use when BS 2700is transmitting data/information to WT 2800. Downlink channels mayinclude downlink traffic channels and assignment channels, each downlinkchannel including one or more logical tone, each logical tone followinga downlink hopping sequence, which is synchronized between each sectorof the cell.

User info 2836 also includes terminal ID information 2842, which is abase station 2700 assigned identification, base station ID information2844 which identifies the specific base station 2700 that WT hasestablished communications with, and sector ID info 2846 whichidentifies the specific sector of the cell where WT 2700 is presentlylocated. Base station ID 2844 provides a cell slope value and sector IDinfo 2846 provides a sector index type; the cell slope value and sectorindex type may be used to derive tone hopping sequences. Modeinformation 2848 also included in user info 2836 identifies whether theWT 2800 is in sleep mode, hold mode, or on mode.

Tone subset allocation sequence information 2850 includes downlinkstrip-symbol time information 2852 and downlink tone information 2854.Downlink strip-symbol time information 2852 include the framesynchronization structure information, such as the superslot,beaconslot, and ultraslot structure information and informationspecifying whether a given symbol period is a strip-symbol period, andif so, the index of the strip-symbol period and whether the strip-symbolis a resetting point to truncate the tone subset allocation sequenceused by the base station. Downlink tone info 2854 includes informationincluding a carrier frequency assigned to the base station 2700, thenumber and frequency of tones, and the set of tone subsets to beallocated to the strip-symbol periods, and other cell and sectorspecific values such as slope, slope index and sector type.

Routines 2820 include communications routines 2824 and wireless terminalcontrol routines 2826. Communications routines 2824 control the variouscommunications protocols used by WT 2800. For example, communicationsroutines 2824 may enable communicating via a wide area network (e.g.,with base station 2700) and/or a local area peer-to-peer network (e.g.,directly with disparate wireless terminal(s)). By way of furtherexample, communications routines 2824 may enable receiving a broadcastsignal (e.g., from base station 2700). Wireless terminal controlroutines 2826 control basic wireless terminal 2800 functionalityincluding the control of the receiver 2802 and transmitter 2804.

With reference to FIG. 29, illustrated is a system 2900 that enablescommunicating with allocated power levels. For example, system 2900 canreside at least partially within a base station. It is to be appreciatedthat system 2900 is represented as including functional blocks, whichmay be functional blocks that represent functions implemented by aprocessor, software, or combination thereof (e.g., firmware). System2900 includes a logical grouping 2902 of electrical components that canact in conjunction. For instance, logical grouping 2902 can include anelectrical component for transmitting on a first channel at a firstpower level from a first sector during a first time period based on afirst predetermined pattern 2904. For instance, the first channel caninclude a first frequency bandwidth. Further, logical grouping 2902 cancomprise an electrical component for transmitting on the first channelat a second power level from the first sector during a second timeperiod based on the first predetermined pattern 2906. The second powerlevel, for example, can be at least 0.5 dB different from the firstpower level. Additionally, system 2900 can include a memory 2908 thatretains instructions for executing functions associated with electricalcomponents 2904 and 2906. While shown as being external to memory 2908,it is to be understood that one or more of electrical components 2904and 2906 can exist within memory 2908.

With reference to FIG. 30, illustrated is a system 3000 that enablescommunicating with allocated power levels in a multiple carrier wirelesscommunication network. For example, system 3000 can reside at leastpartially within a base station. It is to be appreciated that system3000 is represented as including functional blocks, which may befunctional blocks that represent functions implemented by a processor,software, or combination thereof (e.g., firmware). System 3000 includesa logical grouping 3002 of electrical components that can act inconjunction. For instance, logical grouping 3002 can include anelectrical component for transmitting on a first channel at a firstpower level from a first sector during a first time period based on afirst predetermined pattern 3004. For instance, the first channel caninclude a first frequency bandwidth. Further, logical grouping 3002 cancomprise an electrical component for transmitting on the first channelat a second power level from the first sector during a second timeperiod based on the first predetermined pattern 3006. Moreover, logicalgrouping 3002 can include an electrical component for transmitting on asecond channel at a third power level from the first sector during thefirst time period based on a second predetermined pattern 3008. Thesecond channel, for example, can include a second frequency bandwidththat does not overlap with the first frequency bandwidth in frequency.Logical grouping 3002 can also include an electrical component fortransmitting on the second channel at a fourth power level from thefirst sector during the second time period based on the secondpredetermined pattern 3010. Additionally, system 3000 can include amemory 3012 that retains instructions for executing functions associatedwith electrical components 3004, 3006, 3008, and 3010. While shown asbeing external to memory 3012, it is to be understood that one or moreof electrical components 3004, 3006, 3008, and 3010 can exist withinmemory 3012.

When the embodiments are implemented in software, firmware, middlewareor microcode, program code or code segments, they may be stored in amachine-readable medium, such as a storage component. A code segment mayrepresent a procedure, a function, a subprogram, a program, a routine, asubroutine, a module, a software package, a class, or any combination ofinstructions, data structures, or program statements. A code segment maybe coupled to another code segment or a hardware circuit by passingand/or receiving information, data, arguments, parameters, or memorycontents. Information, arguments, parameters, data, etc. may be passed,forwarded, or transmitted using any suitable means including memorysharing, message passing, token passing, network transmission, etc.

For a software implementation, the techniques described herein may beimplemented with modules (e.g., procedures, functions, and so on) thatperform the functions described herein. The software codes may be storedin memory units and executed by processors. The memory unit may beimplemented within the processor or external to the processor, in whichcase it can be communicatively coupled to the processor via variousmeans as is known in the art.

What has been described above includes examples of one or moreembodiments. It is, of course, not possible to describe everyconceivable combination of components or methodologies for purposes ofdescribing the aforementioned embodiments, but one of ordinary skill inthe art may recognize that many further combinations and permutations ofvarious embodiments are possible. Accordingly, the described embodimentsare intended to embrace all such alterations, modifications andvariations that fall within the spirit and scope of the appended claims.Furthermore, to the extent that the term “includes” is used in eitherthe detailed description or the claims, such term is intended to beinclusive in a manner similar to the term “comprising” as “comprising”is interpreted when employed as a transitional word in a claim.

1. A method that facilitates operating a communication network includinga first wireless communication base station that includes a firstsector, comprising: transmitting on a first channel at a firsttransmission power level from the first sector during a first timeperiod, said first transmission power level being based on a firstpredetermined transmission power pattern that indicates a first patternfor varying transmission power as a function of time, the first channelincluding a first frequency bandwidth; and transmitting on the firstchannel at a second transmission power level from the first sectorduring a second time period, said second transmission power level beingbased on the first predetermined transmission power pattern, the secondtransmission power level being at least 0.5 dB different from the firsttransmission power level, wherein the first wireless communication basestation includes a second sector, further comprising: transmitting on asecond channel at a third transmission power level from the secondsector during the first time period, said third transmission power levelbeing based on a second predetermined transmission power pattern thatindicates a second pattern for varying transmission power as a functionof time, the second channel including a second frequency bandwidth, thefirst frequency bandwidth and second frequency bandwidth having at least50% frequency bandwidth in common; and transmitting on the secondchannel at a fourth transmission power level from the second sectorduring the second time period, said fourth transmission power levelbeing based on the second predetermined transmission power pattern, thefourth transmission power level being at least 0.5 dB different from thethird transmission power level.
 2. The method of claim 1, furthercomprising: receiving a channel quality report from a mobile device;scheduling the first channel as a function of the channel qualityreport; and transmitting on the first channel to the mobile device. 3.The method of claim 1, wherein the first transmission power level iswithin 0.5 dB of the third transmission power level, and the secondtransmission power level is within 0.5 dB of the fourth transmissionpower level.
 4. The method of claim 1, wherein the first and the secondpredetermined transmission power patterns are substantially similar. 5.The method of claim 1, wherein the communication network includes asecond wireless communication base station that includes a secondsector, the method further comprising: transmitting on a second channelat a third transmission power level from the second sector during thefirst time period, said third transmission power level being based on asecond predetermined transmission power pattern, the second channelincluding a second frequency bandwidth, the first frequency bandwidthand second frequency bandwidth having at least 50% frequency bandwidthin common; and transmitting on the second channel at a fourthtransmission power level from the second sector during the second timeperiod, said fourth transmission power level being based on the secondpredetermined transmission power pattern, the fourth transmission powerlevel is being at least 0.5 dB different from the third transmissionpower level.
 6. The method of claim 5, wherein the first powertransmission level is at least 0.5 dB greater than the thirdtransmission power level, and the second transmission power level is atleast 0.5 dB less than the fourth transmission power level.
 7. Themethod of claim 5, wherein the first and the second predeterminedtransmission power patterns are periodical with dissimilar differentperiods.
 8. The method of claim 5, wherein the first and the secondpredetermined transmission power patterns are periodical withsubstantially similar periods and different phases.
 9. A wirelesscommunications apparatus, comprising: a memory that retains instructionsrelated to transmitting on a first channel at a first transmission powerlevel from a first sector during a first time period, said firsttransmission power level being based on a first predeterminedtransmission power pattern that indicates a first pattern for varyingtransmission power as a function of time and transmitting on the firstchannel at a second transmission power level from the first sectorduring a second time period, said second transmission power level beingbased on the first predetermined transmission power pattern, the secondtransmission power level is being at least 0.5 dB different from thefirst transmission power level, wherein the memory further retainsinstructions related to transmitting on a second channel at a thirdtransmission power level from a second sector during the first timeperiod, said third transmission power level being based on a secondpredetermined transmission power pattern and transmitting on the secondchannel at a fourth transmission power level from the second sectorduring the second time period, said fourth transmission power levelbeing based on the second predetermined transmission power pattern,wherein the second channel includes a second frequency bandwidth, thefirst frequency bandwidth and the second frequency bandwidth having atleast 50% frequency bandwidth in common, and the fourth transmissionpower level being at least 0.5 dB different from the third transmissionpower level; and a processor, coupled to the memory, configured toexecute the instructions retained in the memory.
 10. The wirelesscommunications apparatus of claim 9, wherein the memory further retainsinstructions for obtaining a channel quality report from a mobiledevice, scheduling the first channel as a function of the channelquality report, and transmitting on the first channel to the mobiledevice.
 11. The wireless communications apparatus of claim 9, wherein afirst wireless communications base station includes the first sector andthe second sector.
 12. The wireless communications apparatus of claim 9,wherein a first wireless communications base station includes the firstsector and a second wireless communications base station includes thesecond sector.
 13. The wireless communications apparatus of claim 9,wherein the first and the second predetermined transmission powerpatterns are substantially similar.
 14. The wireless communicationsapparatus of claim 9, wherein the first and the second predeterminedtransmission patterns are periodical with different periods.
 15. Thewireless communications apparatus of claim 9, wherein the first and thesecond predetermined transmission power patterns are periodical withsubstantially similar periods and different phases.
 16. A wirelesscommunications apparatus that enables communicating with allocated powerlevels, comprising: means for transmitting on a first channel at a firsttransmission power level from a first sector during a first time period,said first transmission power level being based on a first predeterminedtransmission power pattern that indicates a first pattern for varyingtransmission power as a function of time, the first channel including afirst frequency bandwidth; means for transmitting on the first channelat a second transmission power level from the first sector during asecond time period, said second transmission power level being based onthe first predetermined transmission power pattern, the secondtransmission power level being at least 0.5 dB different from the firsttransmission power level; means for transmitting on a second channel ata third transmission power level from a second sector during the firsttime period, said third transmission power level being based on a secondpredetermined transmission power pattern, the second channel including asecond frequency bandwidth, the first frequency bandwidth and the secondfrequency bandwidth having at least 50% frequency bandwidth in common;and means for transmitting on the second channel at a fourthtransmission power level from the second sector during the second timeperiod, said fourth transmission power level being based on the secondpredetermined transmission power pattern, the fourth transmission powerlevel being at least 0.5 dB different from the third transmission powerlevel.
 17. The wireless communications apparatus of claim 16, furthercomprising: means for obtaining a channel quality report from a mobiledevice; means for scheduling the first channel as a function of thechannel quality report; and means for transmitting on the first channelto the mobile device.
 18. The wireless communications apparatus of claim16, wherein the first and the second predetermined transmission powerpatterns are periodical and have at least one of disparate periods anddisparate phases.
 19. A non-transitory machine-readable medium havingstored thereon machine-executable instructions which when executed by aprocessor control a communications device to perform the steps of:transmitting on a first channel at a first transmission power level froma first sector during a first time period, said first transmission powerlevel being based on a first predetermined transmission power patternthat indicates a first pattern for varying transmission power as afunction of time, the first channel including a first frequencybandwidth; transmitting on the first channel at a second transmissionpower level from the first sector during a second time period, saidsecond transmission power level being based on the first predeterminedtransmission power pattern, the second transmission power level being atleast 0.5 dB different from the first transmission power level;transmitting on a second channel at a third transmission power levelfrom a second sector during the first time period, said thirdtransmission power level being based on a second predeterminedtransmission power pattern, the second channel including a secondfrequency bandwidth, the first frequency bandwidth and the secondfrequency bandwidth having at least 50% frequency bandwidth in common;and transmitting on the second channel at a fourth transmission powerlevel from the second sector during the second time period, said fourthtransmission power level being based on the second predeterminedtransmission power pattern, the fourth transmission power level is beingat least 0.5 dB different from the third transmission power level, thefirst predetermined transmission power pattern and the secondpredetermined transmission power pattern are periodical and have atleast one of disparate periods and different phases.
 20. Thenon-transitory machine-readable medium of claim 19, themachine-executable instructions further comprising instructions forcontrolling the communications device to perform the steps of: receivinga channel quality report from a mobile device; scheduling the firstchannel as a function of the channel quality report; and transmitting onthe first channel to the mobile device.
 21. In a wireless communicationssystem, an apparatus comprising: a processor configured to: transmit ona first channel at a first transmission power level during a first timeperiod, said first transmission power level being based on a firstpredetermined transmission power pattern, the first channel including afirst frequency bandwidth; transmit on the first channel at a secondtransmission power level during a second time period, said secondtransmission power level being based on the first predeterminedtransmission power pattern, the second transmission power level is beingat least 0.5 dB different from the first transmission power level;transmitting on a second channel at a third transmission power levelfrom the second sector during the first time period, said thirdtransmission power level being based on a second predeterminedtransmission power pattern that indicates a second pattern for varyingtransmission power as a function of time, the second channel including asecond frequency bandwidth, the first frequency bandwidth and secondfrequency bandwidth having at least 50% frequency bandwidth in common;and transmitting on the second channel at a fourth transmission powerlevel from the second sector during the second time period, said fourthtransmission power level being based on the second predeterminedtransmission power pattern, the fourth transmission power level being atleast 0.5 dB different from the third transmission power level.
 22. Themethod of claim 1, wherein said steps of: i) transmitting on a firstchannel at a first transmission power level and ii) transmitting on afirst channel at a second transmission power level are performed using asingle antenna, the same single antenna being used for each of saidrecited transmitting steps.
 23. The wireless communications apparatus ofclaim 9, further comprising: a single transmitter; and wherein saidtransmitting on a first channel at a first transmission power level andsaid transmitting on a first channel at a second transmission powerlevel are performed using said single transmitter antenna.
 24. Thenon-transitory machine-readable medium of claim 19, wherein saidprocessor executable instructions further include instructions forcontrolling said communications device to use a single transmit antennafor transmitting on a first channel at a first transmission power leveland transmitting on a first channel at a second transmission powerlevel.
 25. The apparatus of claim 21, further comprising: a singletransmitter antenna; and wherein said processor is configured to usesaid single antenna for transmitting on a first channel at a firsttransmission power level and transmitting on a first channel at a secondtransmission power level.